Doesn't God giving orders to demons contradict the principle of double effect?

It is true that ends do not justify means (Rom. 3:8: one can "not do evil that there may come good"), but, as St. Thomas Aquinas writes in Summa Theologica I q. 114 a. 1 ad 1,

the demons who are sent to punish, do so with an intention other than that for which they are sent; for they punish from hatred or envy; whereas they are sent by God on account of His justice.

^{Daemones ad puniendum missi, alia intentione puniunt, quam mittantur, nam ipsi puniunt ex odio vel invidia; mittuntur autem a Deo propter eius iustitiam.}

God's good intention of exercising justice does not become evil just because the demons' intention is evil.

^{For example, an employer's good intention that his employees make a good product does not become evil if the employees' intention is to make money for an evil purpose (e.g., to buy illegal drugs).}

Also, demons are angels (creatures), and creatures are good (1 Tim. 4:4: "For every creature of God is good"). So, God is not doing evil or sinning by holding demons in existence.

There is a sinful, human notion that "the end justifies the means", which runs hand in glove with the equally sinful, human notion that "might is right". When humans start with such flawed, ungodly ideas in mind, then suppose that some isolated bits in the Bible appear to show God working along very similar lines, then questions such as this arise.

A good way to answer this in a helpful manner is to start with the greatest (God) and then compare the lesser (sinful humanity) with their creator - God. Sadly (though understandably) most people start with human ideas. Well, if we start with God we begin with the perfection, justice, righteousness, holiness and love of God; the concepts to be grasped are of light and truth and unchangeableness and sovereignty. Also, it's vital to realise that God created everything, material and immaterial, including a material universe with this planet packed full of life and provisioned so that the pinnacle of God's creation on earth - humans created in God's image and likeness - lacked for nothing. God's immaterial spirit creations (called angels, some of whom became demons due to rebelling against their creator, as did humanity) are just as much subject to the sovereignty of their creator as are humans.

You will notice that I'm not paying much attention to what you call "the principle of double effect". That's because it's not a biblical concept. As you ask this in the Christianity section, I suggest that the answers come from what the holy scriptures say, and not from the realms of human philosophy.

The Bible shows time and again God exercising his sovereign right as creator to bring about his will to pass, despite all that humans and demons try to achieve. He fools people at times. (He fooled me before I became a Christian in order to bring me to saving faith in Christ, and he can fool me any time he likes, though that's too easy for words!) He keeps people in the dark (spiritually speaking) when their hearts are darkened and hardened against him. That's his prerogative. He's the Almighty.

God uses world rulers to carry out his will at particular times. He even uses them to bring down other world rulers that seem to be thwarting God's will. He changes the course of history - never more so than by bringing his only-begotten into the world to defeat sin, death and the devil at Golgotha and the empty tomb.

He has also told us in advance what he is going to do (and even now is in process of doing) culminating in the spectacularly unexpected return of Christ to usher in the awesome Day of Resurrection and Judgment. You can read all about that in the last book of the Bible, penned shortly before the end of the first century A.D. That book fearfully shows God exercising his sovereign will over human governments, religions, and Satan with his hordes.

When your question is looked at from such a radically different perspective, you may see the need to stick to what the holy scriptures say about our creator. Then Jesus commanding the demons when he walked this earth, and their inability to disobey him, shows the sovereignty of God. Every knee will have to bend before Jesus, who has the name above every name (Philippians 2:9), many unwillingly on the Day of Judgment, but those who belong to him by faith willingly, at the point of them trusting only in Christ. I hope this help you.

OP has said in a comment, "And it seems to be reasonable that it is not right to bring good through evil ".

The greatest evil ever perpetrated was the murder by the Romans, at the request of the Jewish leaders, of the only truly innocent human being who ever lived.

The greatest good ever perpetrated was the redemption of mankind through the death, burial, and resurrection of that same one.

Both of these things happened according to the council and foreknowledge of God:

Him, being delivered by the determinate counsel and foreknowledge of God, ye have taken, and by wicked hands have crucified and slain: - Acts 2:23

It is reasonable and right for God (who alone is good) to bring good through evil (which is absence of good just as darkness is absence of light (cf John 1:4-5, 2 Cor. 4:3-4)). In fact, there is no one else who can:

And Joseph said unto them, Fear not: for am I in the place of God? But as for you, ye thought evil against me; but God meant it unto good, to bring to pass, as it is this day, to save much people alive. - Genesis 50:19-20