I completed the introductory level and i still don't fully understand the mechanics.
I think the cats go back in the direction they came from but will move into a house if they end up next to it.
I guess i have some confusion i'll explain with the challenge level 1. (Letters are Horizontal, Numbers Vertical)
Warrior cats can't seem to push the diagonal cat twice. Placing the fish underneath that cat twice only seems to cause 1 push if done by the same warrior cat. Moves where Fish C4 and Fish C3 afterwards. Fish C4 and Fish B2 also causes no second push while Fish C3 and Fish D4 causes a push. I don't understand why it works sometimes and doesn't work in other times.
I also don't get why Fish C2 doesn't get the diagonal cat into the box but placing a Fish B2 causes the interaction to happen.