Is a familiar compelled when their wizard is?

I have a party and an aboleth dominated them (only two players present). The aboleth didn’t do anything to the wizard’s familiar. Does the wizard’s familiar get affected by the compulsion effect too? Would a familiar always know if their wizard was affected by a compulsion? (In my case the aboleth was out of view and hearing when casting)

In play I ruled that the familiar could act freely, as it had a reasonable intelligence score (Int 8 for wiz level 5). It tried to save its wizard but failed. Eventually the aboleth told the wizard to reign in their familiar. Now the party has a new subterranean "quest giver."