I had the same problem with the water bottle I used for my bunny. When you fill it, put the cover on and leave it facing down and push the bally thing up with your finger letting some of the water out. That seemed to make the proper vacuum it needed so it wouldn't leak. I returned a few before I realized I had to do this. Try it, I hope it works.
Good luck with Eddie. My Wally was afraid of the stainless bowl also. He saw his little reflection and it scared him