I don't think it's ref or technical rooms fault in that very occasion, If you ask me, but the first problem was both team players being an utter distraction for the referee, in most cases of handballs or foul in the 12 yard box, the VAR crew probably always have a verdict of their own imo, but the players just need to allow the referee breathing space, it took the referee way less to come to a conclusion after checking the replay, probably around 5 secs or thereabout from him looking at the screen, when it comes to goals being ruled or not for offside that's the VAR team decision to make, but for handballs, fouls, and red card worthy offences the referee is sole decision maker, VAR crew are just meant to call is attention to it if he didn't make the call at first glance imo, but the team players all ranting at once wouldn't even allow the referee communicate properly with the VAR team. If you look at Matip's low header that looks like it touched his hands some moments before Man City equalised, the VAR probably looked at it and since there probably no contact to his hands, the referee had no reason to come into play, the scenario didn't get replayed all through the end of the game, so It made me pretty sure there was probably nothing to be looked at in that case. More so, the players are always the ones begging the referees to take a look for themselves.
It's getting silly. It's a coin toss as to what is handball these days. It's also really annoying how they delay the kick off after almost every single goal whilst VAR checks every possible parameter they can to possibly disallow it. They need to scrap the ref going over to have a look at the little screen as well. Why do you need him to go over and decide when you've already got several officials watching the game on several big screens? Just let them decide. If they think something is wrong then it's likely the ref will as well.