Like all English words, the use of “who’s” and “whose” depends on the context.
“Who’s” is the contracted form of “who is”, and is used to decipher who the performer of an action is.
For example, “who’s on the phone?”
“Whose” is a determiner used to denote belonging. In other words, it is used when trying to find out whom something belongs to.
For example, “whose bag is this?”, or “whose house is that?”
When in doubt, expand/ separate “who’s” into two words: “who is” and recheck the sentence. If it fits into the sentence, then the context is right.