Is it logical to tell atheists to "prove god(s) does not exist"?
No, it is not logical. No one goes around proving a negative.
No one in his right sanity goes around proving a negative.
There is no empirical evidence to start with. There is NOTHING to start with. So how we supposed to prove the non-existence of a negative?
Take for example a fairy.
Fairies have been mentioned in books, in many cultures and even believed and worshiped by people. Yet there is NOT a single shred of empirical evidence to prove that fairies exist.
So now, do we ask scientists to prove the non-existence of fairies?
How are we supposed to prove a negative when there's nothing there?
If someone claims he/she encountered a fairy, it is UP to the claimant to prove his/her claim. He/she should not be asking others to prove that fairies don't exist.
It's just illogical.