I have the same exact problem with my cat. I rent also and when I moved out of my apartment in June they didn't charge me for the damage because they said the carpet needed replacing anyways. So I was lucky that time.
I currently live in a new place and my cat will do that too and it's...
Oh my goodness Shiraz, one of my cats does exactly the same thing (spilling water) and it drives me nutts. She is a little over a year old and does it when drinking then afterwards plays with it and topples it over. I have one other cat and do the same thing have other little bowls of water so...