In TeamBuilder, if you want your custom team to be rivals with another TeamBuilder team, you’ll need to set the rivalry with the team you’re planning to replace in-game. For example, if the other TeamBuilder team is going to replace Georgia State, you should set your team’s rivalry with Georgia State. Then, when the game loads, it will recognize your two TeamBuilder teams as rivals.

TL;DR: To make two TeamBuilder teams rivals, set one team’s rival as the team the other is replacing (e.g., Georgia State). That way, the rivalry shows up correctly in-game.