"Great video!"
It is informative all right but if someone spends that much time dicking with an ETA 2892 they will starve to death...unless they charge $500 for a tune up. Imho.
I have known three (3) bonafide pro watch repair guys that are capable of that kind of work but they could not afford it (takes too long) and the customer can't either.
So...since I work mostly on 'trader junk,' I'll make a guess as to what is wrong with the ETA in question:
1...Magnetized. Maybe.
2...Dirty or oily hairspring. Maybe.
Something is making the watch run too fast and the two things above are common culprits but usually cause more gain per hour than 4 minutes.
Check the reserve by removing the autowind assembly (to get it out of the way and save wear on reversers when hand winding), then hand wind it 35 or 40 turns to see how long it runs and check it in 24 hours to see how much time it has gained and if the balance motion appears to be much more sluggish than when fully wound (a little bit can be expected). When hand winding, turn the crown until you can feel the bridle slip in the mainspring barrel to make sure it is slipping because if it is sticky or not slipping it will cause the watch to run fast when fully wound because the MS can not slip to release tension on the time train. Sometimes a weak mainspring will not supply enough power to give the balance a good 'kick' and this can result in a short, choppy 'kick' also causing the watch too run fast.
Btw...did you see any dark specks on the cap jewels at all? If so, they have to be removed and the hole jewels also have to be super clean. Rub the cap jewel over a business card etc to remove any residue after cleaning it, before oiling it. Oil only the cap jewel (about 2/3 of its area, centered) and lay the hole jewel/setting on top of it, put it in place, close the spring/keeper. Harder to do than oiling the balance staff where it pokes through the hole jewel then setting the cap jewel on top of it but that is not the proper way to do it imho because the oil can travel away from the hole jewel. It stays on the cap jewel a lot better.
When it is running after being fully wound, see if the balance has good balance motion (degrees of motion) and if the balance is 'frisky' and has a good 'kick' or 'lazy' with a weak 'kick' and not a whole lot of motion. A lazy 'kick' can result in gaining time because the balance starts to 'short stroke' and not give a full 'kick'. If it is 'kicking' too hard and fast it will run fast.
Four minutes gain in an hour is not a whole lot so the problem ight be hard to find compared to gaining 20 minutes per hour etc.
Troubles like this are why I usually wear an Accutron II.