Who really fired on Ft. Sumter - the South or Local Charleston, SC militia?

Actually it was the South Carolina militia which fired first. Several levels of the command structure ending in the first cannon shot fired by Lieutenant Henry S. Farley were all from South Carolina.

THE FIRST SHOT ON FORT SUMTER.
The battery on the beach, or east, was under the immediate command of Captain James, with Lieutenant Henry S.º Farley as lieutenant, and the battery on the hill, or west, was under the immediate command of Lieutenant Indicates a West Point graduate and gives his Class.Wade Hampton Gibbes, I think with Lieutenant J. McPherson Washington as next, and the company of infantry, as reserves, was commanded by Lieutenant Theodore B. Hayne, and was stationed near the old Martello Tower, about 400 p143 yards in the woods, to the northwest of the hill, or Gibbes, battery.

Lieutenant Henry S. Farley who fired the first shot was from South Carolina. commanded by Captain George S. James, South Carolina State troops commanded by Lieutenant J. McPherson Washington also from South Carolina

Lieutenant Henry S. Farley, the commander a battery of two 10 inch siege mortars on James Island is credited with firing the first shots at Fort Sumter at 4:30 a.m.

However to support @Giter's conclusion above. Why does the origin of those troops who fired the first shot mean anything? The States had seceded, the Confederate General Beauregard was in charge and had issued a demand to the federal government to surrender the fort. Both sides knew what was about to happen an both sides know the Union fort was facing the unified secessionist states under the overall command of Beauregard.

The fact South Carolina troops fired first probable was an honor accorded to SC being the first state to succeed or Fort Sumter being within the borders of their state, or both. Suggesting South Carolina started a war the South didn't want is not really supported by the facts.

The bombardment of fort Sumter went on for 34 straight hours. That involved a lot more troops, cannons and powder than just the SC batteries.

Lastly all that shooting by the Confederates didn't kill a single Union soldier. So if it was all a mistake, the South certainly had the opportunity to correct the "misunderstanding" afterwards...

No this was the first offensive action of the civil war, perpetrated by the South collectively (the states which had succeeded up to that point) upon the Union forces which they deemed were now unwelcome in their secessionist and independent states.

(*). Two union solders died at fort Sumter, both occurred after the Union had surrendered as the Union troops were giving themselves a 100 gun salute prior to retreating from the field of battle, per terms of surrender. One of their cannons blew up.

On December 20, South Carolina declared that it seceded. Six days later, Union Major Robert Anderson moved his troops into Fort Sumter.

A letter by South Carolina Governor Francis Pickens to President Buchanan on January 31st demanded that the fort be surrendered. It, along with more messages demanding surrender, were ignored.

On April 11, the amazingly named Confederate Brigadier General Pierre Gustave Toutant-Beauregard sent Colonel James Chestnut to demand the surrender of the fort, and to negotiate conditions for surrender. When that failed, on April 12 Confederate batteries opened fire on the fort, and the war began.

So, instead of 'a bunch of angry local guys who drank too much ale', it was a Confederate colonel and his troops acting under official orders of a Confederate general, several months after the state declared secession. Thus, it was an official attack by a technically sovereign state(which you call 'The South').