When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.
I'm pretty sure it should shut off as, mine does the same as yours. staying on wouldn't do a bit of good, water flow stops when the engine is shut off.
I could have sworn the sticker on the inside of the hood say "be careful fan comes on when car is off" maybe that would be a malfunction?
And although there is no water cooling, that fan does a lot of work. I Know black magic fans, I had one on my mustang that stayed on until my stang was cool enough. My girls saab also does the same.