Well, in both cases, the people were late after intermission, not to the start of the show.
During Rent, they started Seasons of Love even though it was clear everyone wasn't in their seats. Since the curtain went up late (there is no curtain, but you know what I mean) I think they wanted to just get the ball rolling. For Company, Raul was standing at the edge of the stage and just like blatantly watched them all until they got to their seats. It was actually funny.
It's intimidating to know that he's that aware of audiences all the time. Most actors say that they can tell what kind of night it will be by the audience's reaction right away. But by the same token, the audience paid money to see the performance, and there should be a certain standard to fulfill even if it's a theater full of duds
The morning star always gets wonderful bright the minute before it has to go --doesn't it?