The OP said this in a comment:

technically speaking, Spain was a satellite state. However, the treaty was mainly intended for the countries within the big blocks so I assume it was just ignored.

The second statement, that Spain was overlooked, is flatly not true as will be demonstrated once we look at the text of the agreements and the historical arguing about what to do with Spain.

The question of whether Spain counted as an Axis satellite state is one which was hotly debated in 1944 and 1945. This is the crux of the question.

What The Yalta Agreement Said

"Axis satellite state" is mentioned in the "Protocol Of Proceedings Of Crimea Conference", aka the Yalta Agreement, but it's never defined.

They jointly declare their mutual agreement to concert during the temporary period of instability in liberated Europe the policies of their three Governments in assisting the peoples liberated from the domination of Nazi Germany and the peoples of the former Axis satellite states of Europe to solve by democratic means their pressing political and economic problems.

However, section II "Declaration Of Liberated Europe" makes it clear what their goals were. It's worth reading in its entirety. Italics are mine to highlight relevant sections.

The Premier of the Union of Soviet Socialist Republics, the Prime Minister of the United Kingdom and the President of the United States of America have consulted with each other in the common interests of the people of their countries and those of liberated Europe. They jointly declare their mutual agreement to concert during the temporary period of instability in liberated Europe the policies of their three Governments in assisting the peoples liberated from the domination of Nazi Germany and the peoples of the former Axis satellite states of Europe to solve by democratic means their pressing political and economic problems.

The establishment of order in Europe and the rebuilding of national economic life must be achieved by processes which will enable the liberated peoples to destroy the last vestiges of nazism and fascism and to create democratic institutions of their own choice. This is a principle of the Atlantic Charter - the right of all people to choose the form of government under which they will live - the restoration of sovereign rights and self-government to those peoples who have been forcibly deprived to them by the aggressor nations.

To foster the conditions in which the liberated people may exercise these rights, the three governments will jointly assist the people in any European liberated state or former Axis state in Europe where, in their judgment conditions require,

(a) to establish conditions of internal peace;

(b) to carry out emergency relief measures for the relief of distressed peoples;

(c) to form interim governmental authorities broadly representative of all democratic elements in the population and pledged to the earliest possible establishment through free elections of Governments responsive to the will of the people; and

(d) to facilitate where necessary the holding of such elections.

The three Governments will consult the other United Nations and provisional authorities or other Governments in Europe when matters of direct interest to them are under consideration.

When, in the opinion of the three Governments, conditions in any European liberated state or former Axis satellite in Europe make such action necessary, they will immediately consult together on the measure necessary to discharge the joint responsibilities set forth in this declaration.

By this declaration we reaffirm our faith in the principles of the Atlantic Charter, our pledge in the Declaration by the United Nations and our determination to build in cooperation with other peace-loving nations world order, under law, dedicated to peace, security, freedom and general well-being of all mankind.

This isn't a denunciation of fascism. It isn't a call to arms to overthrow dictatorships worldwide. It's defining how the liberated nations and minor Axis powers will be treated after WWII.

The goal is "to solve by democratic means their pressing political and economic problems". Someplace like Romania, Hungary, or Bulgaria, Axis belligerents who were devastated by the war. Or Norway and the Netherlands who had puppet governments installed. These countries needed their governments replaced, economies rebuilt, and social order restored.

Spain, in contrast, was neither conquered by the Axis nor allied with them. They never declared war and they never allowed either power to move troops through their country (to the great relief of Britain and Gibraltar). Spain had a working, independent, if fascist, government. They were untouched by the war. By the scale of the rest of Europe they had no "pressing political and economic problems".

Was Spain an Axis Satellite?

This is not to say people didn't try to get Spain treated as an Axis satellite state. Spain was technically "non-belligerent" but they really, really pushed it. The Spanish civil war, a proxy battle between communism and fascism, and their support of the Nazis made Spain a hot button topic for communists and socialists after the war. In particular the French and the Soviets.

While Spain never officially sent Spanish troops to fight, they allowed an entire division of volunteers to fight the Soviets. The 250. Infanterie-Division aka División Española de Voluntarios aka División Azul (curiously, their emblem is red and yellow) was an all volunteer division, some professional soldiers, some anti-communists, trained and supplied by the Germans, and sent to fight on the Eastern Front in 1941. They fought in the Siege of Leningrad and earned the Soviet's ire by stopping a major attempt to break the siege in 1943. Eventually almost 50,000 Spaniards would fight the Soviets.

Pressed by the Allies, Franco ordered all volunteers to return to Spain in late 1943. This is an important point, by 1944 Franco could see the writing on the wall and was more and more cooperating with the Allies.

But many wanted to see Spain excluded from the growing United Nations. At the UN Conference on International Organization...

the Mexican delegate to the conference, a Spanish exiled anti-fascist named Luis Quintanilla, appealed for the exclusion of Spain from the UN on the grounds that the United Charter excluded all those countries ruled by regimes established with the help of Germany or Italy.

At the later Potsdam Conference in 1945...

the Soviets wanted to go one step further and proposed on 19 July 1945 that all relations with Franco including diplomatic and economic links be severed.

The eventual statement was a bit softer.

In a joint statement, issued during the Potsdam Conference, the three great powers, US, Britain and the USSR, expressed their wish that Spain should not apply for membership to the United Nations given the fact that her current regime was founded with the help of the Axis powers, was closely associated with the Axis and did not posses the necessary qualifications to justify membership

The strongest statement made was the Tripartite Statement on Spain of March 4, 1946...

THE GOVERNMENTS of France, the United Kingdom, and the United States of America have exchanged views with regard to the present Spanish Government and their relations with that regime. It is agreed that so long as General Franco continues in control of Spain, the Spanish people cannot anticipate full and cordial association with those nations of the world which have, by common effort, brought defeat to German Nazism and Italian Fascism, which aided the present Spanish regime in its rise to power and after which the regime was patterned.

However this declaration had no teeth because it was considered an internal Spanish problem.

There is no intention of interfering in the internal affairs of Spain. The Spanish people themselves must in the long run work out their own destiny. In spite of the present regime's repressive measures against orderly efforts of the Spanish people to organize and give expression to their political aspirations, the three Governments are hopeful that the Spanish people will not again be subjected to the horrors and bitterness of civil strife.

But the idea of diplomatic and economic sanctions was floated.

Such recognition would include full diplomatic relations and the taking of such practical measures to assist in the solution of Spain's economic problems as may be practicable in the circumstances prevailing. Such measures are not now possible. The question of the maintenance or termination by the Governments of France the United Kingdom, and the United States of diplomatic relations with the present Spanish regime is a matter to be decided in the light of events and after taking into account the efforts of the Spanish people to achieve their own freedom.

UN Chapter VI: No Invasion Allowed

In 1946, Spain was having a hard time diplomatically.

Worldwide public opinion was moving against Franco. Canada publicly rebuffed Spain’s attempt to establish diplomatic relations. During spring 1946, six Communist, four Latin American, three Commonwealth and four other states severed diplomatic relations with Spain. There was also speculation that Italy might do the same.

Article 33, beginning Chapter VI of the UN charter, says:

The parties to any dispute, the continuance of which is likely to endanger the maintenance of international peace and security, shall, first of all, seek a solution by negotiation, enquiry, mediation, conciliation, arbitration, judicial settlement, resort to regional agencies or arrangements, or other peaceful means of their own choice.

The UN found that the issue of what to do about Spain fell under Chapter VI and thus had to be resolved by peaceful means, didn't matter that Spain was not then a UN member. There could be no invasion of Spain by UN states to topple Franco.

This culminated in December 1946 with UN Resolution 39 "Relations of Members of the United Nations with Spain" which called for the end to the Franco regime and its diplomatic isolation.

Spain may not be admitted to the United Nations...

Recommends that the Franco Government of Spain be debarred from membership in international agencies established by or brought into relationship with the United Nations...

Recommends that all Members of the United Nations immediately recall from Madrid their Ambassadors and Ministers plenipotentiary accredited there.

The Influence of the Cold War

Other sources talk about the desire of the US to take a gentle approach to Spain in order to bring her into the fold of a Western Alliance to defend against Communism. The US military found the prospect of a war and national uprising in Spain dubious saying:

there is no prospect of any form of popular rising taking place in Spain... a rising, caused by foreign intervention, if strong enough to avoid immediate suppression by the police with army backing, would almost inevitably result in the outbreak of another civil war... a civil war in Spain with French and Russian intervention would also be likely to precipitate a crisis in France.

The US military increasingly looked at Spain and Italy as fallback positions against possible Soviet invasion of Europe. The Pincher Plan saw the possibility of using the Pyrenees as a natural defensive line to buy time against an overwhelming Soviet attack for a US build up.

The withdrawal of US forces across France into Spain also may prove feasible. This, too, will be largely dependent upon political considerations. It is probable that an anti-Communistic government will remain in power for at least the next year or two, and if Spain is willing to desert her position as a neutral, then the withdrawal of US forces into Spain would make a material contribution to any required defense of the Pyrenees. On the other hand, the Allies would probably be committed to the defense of Spain, which might well entail a substantial diversion of resources. Retention of an anti-Communist government in Spain would materially assist in maintaining the security of the western Mediterranean.

Here we see the beginnings of the Cold War idea that if you're anti-Communist, you're a potential US ally. That it's better to support a fascist dictatorship than to risk a left-leaning democratically elected government. Sir Victor Mallet, British Ambassador to Spain, wrote

A weak Government in Spain, whether of the Right or the Left, would pave the way for increased Soviet influence and pressure through the Spanish Communists. The one real merit of the present Government is that it does at least maintain order.

Sources

• International Relations between the U.S. and Spain 1945-53 Economics, Ideology and Compromise (This covers the post-war Spanish narrative in detail)
• The Spanish Government and the Axis from The Avalon Project.