Where do keys go?

Hey,

this question may seem a bit odd at first but i wanted to make sure we play the game correctly. If we get one or more keys where do the go to? Do they appear on one's player board or moved into the storage? Or somewhere completely else? I'm asking since we stumbled over a map action where a player could spend a key instead of intent. She used the key but it felt kind of wrong because I was on another tile (which was clearly seperated from hers). Is this situation intended and the keys can be freely shared?

I tried to look it up in the rules but couldn't find an answer. I'm pretty sure it's written somewhere ;)

Thanks for your help!