Some abilities like Ember purple ability have a interupt effect that is not mentioned in the description. While a lot of them interupt animations no matter what others only do it when they crit. Most noticeable one is Leah split shot, if it crits it can stop abilities that are being cast.
That's not quite true. Every ability has the chance to interrupt. The two main factors here is the correlation between"Physical Attack + Physical Pierce Rating + Physical Crit Rating vs. enemies Physical Armor"
and"Magic Attack + Magic Pierce Rating + Magic Crit Rating vs. enemies Magic Armor"
The greater the difference the more likely is it to crit and make the enemy flinching.