Summary
While in Block Stun, press the controller to Toward and then press the Assist Button that corresponds to the Assist Character you want to jump in and perform their Cross-Over Counter. A Cross-Over Counter costs one Level of Hyper Meter to perform.
Counter Intuitive
Again, the Assist 1 Button will call Assist Character 1 to perform their Cross-Over Counter and the Assist 2 Button will call Assist Character 2 to perform their Cross-Over Counter. The move that is performed is directly tied to the Assist Type that was chosen. Whatever their Cross-Over Assist action is, that's what they will perform when they jump in as a Cross-Over Counter. And yes, that means if your Assist was Morrigan with the Dark Harmonizer, performing a Cross-Over Counter will have Morrigan jump in and give Hyper Meter to herself, leaving herself extremely open to just about any attack you can think of.
Again, because the character jumping in is performing their Cross-Over Assist action, what was said about Cross-Over Assists applies to Cross-Over Counters: they come out slowly and they have very little invulnerability. Proper use of Cross-Over Counters to actually hit the opponent in the middle of their move is very difficult. Usually, the only way to get it to connect is to counter a Normal Move the very instant the opponent chains it into another Normal Move so that the second Normal Move whiffs and you come in and hit them. But even then they can cancel the whiffing Normal Move into Hyper Combo and beat up your Cross-Over Counter.
Strategy Corner
What this means is, essentially, Cross-Over Counters are almost useless being used as an actual counter. What Cross-Over Counters actually turn out to be more useful for are saving the life of a character that is about to be chipped to death without using your X-Factor.