The broadcasts always start at regular times. They allow lead-in for a little introduction and sometimes a pre-game show before the first pitch. Most networks broadcasting the game allow 5-9 minutes. The TBS games always start 7 minutes after the broadcast time, with starts at 8:07 or 4:37 for example. Fox does a longer pre-game, generally starting 27 minutes after the beginning of their broadcast. The game tonight will begin broadcasting at 7:30 with the first pitch at 7:57 on Fox.
In the regular season, the teams decide the game time for their home games and they negotiate with the networks that broadcast the games for the specific time. In the post-season, the teams have nothing to do with it, it's a negotiation between Major League Baseball (the central organization) and the networks. It took a lot of negotiating to get Fox to agree to start the games before 8 PM. It's not far before 8, but it's about half an hour earlier than the Fox broadcasts last year.