In the live update, animal pens are more of a way to... encourage animals to go somewhere. They'll freely leave the pen to go eat/drink. You can lock them inside with the lock utility, but until I can add layers of locking restriction, it will unfortunately lock them in, and everyone else out. Not great for keeping them fed. You can add stockpiles to pens for their food items to be brought in. But, again unfortunately, there is no stockpile priority, so it's not guaranteed these will be kept stocked.
Ok, so that's the bad news. The good new is the next update comes with stricter rules for captured entities (keeping them forced to their rooms), and also adds stockpile priorities. Sorry they are currently a pain to use. That whole system is very much on my radar.