The dominate spell specifies
You take command of the target, forcing it to obey your orders. If you issue an obviously self-destructive order, the target doesn't act until you issue a new order. The effect depends on its Will save.
Critical Success The target is unaffected.
Success The target is stunned 1 as it fights off your commands.
Failure You control the target. It gains the controlled condition, but it can attempt a Will save at the end of each of its turns. On a success, the spell ends.
Critical Failure As a failure, but the target receives a new save only if you give it a new order that is against its nature, such as killing its allies.
The Controlled condition is pretty straightforward
Someone else is making your decisions for you, usually because you're being commanded or magically dominated. The controller dictates how you act and can make you use any of your actions, including attacks, reactions, or even Delay. The controller usually does not have to spend their own actions when controlling you.
I'm guessing the critical failure caveat is a fail-safe to allow a second Save because you do not have access to the repeated Saves granted by Failure, but the text almost reads (as it was in Pathfinder 1e and similar RPG's) that the extra Save against attacking allies was already implied. Mostly curious if I missed any text that would indicate the second (or a different) interpretation.