It depends what team is playing but I still find it surprising how big of an impact a red card in football can have and within minutes turn the whole game completely upside down. After the red card it was only Roma, but then the penalty put the nail in the coffin for Sassuolo regarding their mental resilience. I think they really felt broken at that point because everything in that game turned against them. The second goal was to be expected somehow as Roma was pressing hard for it.
Like you rightly said it really depends on the team, some team do have red card and still manage to win but then again it also depends on the strength of their opponent, a typical example was in the bundesliga were Bayern had a red card yet they won because they has a weaker opponent, the strength of a team has alot to do with how well they cope with situations that arises on the pitch.
Roma had a better strength when compared to sassuolo, it's been seen that in most of the games sasuolo had played this season in the serie A they have struggled to win or gat a draw but in most cases they lost , Roma had been playing on an average scale but then it turned out they are gradually building strength and climbing the league table probably aiming at the top, so the red card in the game against sassuolo was a big advantage for Roma which they didn't fail to use. The psychology of the players no doubts was really affected and it became obvious in their performance.
I think in many cases the teams that can organize a high ball possession play when they are still the full eleven players perhaps have an easier time to play down the clock when they lose a player due to a red card. Control with the ball and determination of the game speed could be the things that are important when being one man less. But Sassuolo is not the team that is known for having outstanding ball control and high possession during games. That's why they fell apart after the red card and Roma exploited that weakness.