First, the use of "communicate" in the original superpower description is presumably referring to communication that couldn't happen without the power - and the side effect uses the same term. As it stands, my dog can tell me she understands I intend to walk her by jumping off the back of the couch and being excited at the door.

So if the superpower only refers to novel communication, I'd interpret that to mean anything more than I could reasonably communicate to my dog, and more than she could communicate to me (confirmation of understanding).

If the side effect, despite using the same verb, actually renders animals LESS able to communicate with me than they already can, that seems an especially uncharitable interpretation.

Alternatively, I can ask the animal to wait until I was out of the room before performing the action for the third party. At that point, only that third party would end up communicating having seen the comprehension/performance.