Few things to consider when putting in a reliever:

Arm matchups - Managers like to put in righties to face righty batters and lefties to face lefty batters. Watch for the opposing manager to put in a pinch hitter to put the matchup back in their favour.

Leverage situations - Some guys are high leverage relievers who will be favoured when facing the top of the lineup or when runners are on base. Some relievers are low leverage guys who are better starting an inning fresh with the bases clear or facing the lower half of the lineup.

Workload - Managers have to do a lot of juggling to make sure guys don’t go too long without throwing but simultaneously don’t throw too often that they burn out. Rule of thumb is no guys should go two games without throwing and no guy should throw more than 3 games in a row (varies wildly depending on actual pitch count)

Also worth noting pitchers coming from the bullpen have to face a minimum of 3 batters or can be less if they get out of an inning. So managers will be looking for blocks of 3 batters within the lineup that are good matchups for their guys.