Can [On Play] effects activate during your opponent’s turn?

I have a small question regarding the [On Play] effect for the new OP10-009 Smiley card. When combined with OP01-069 Caesar’s [On K.O.] effect, you can play the smiley card on your opponent’s turn, therefore activating the [On Play] effect and giving -3000 to one of your opponent’s characters, is this correct? Or do [On Play] effects activate on my turn only? I would assume not unless stated otherwise, like OP03-013 Marco which has both a [Your Turn] and [On Play] attached to the same effect. Am I correct or missing something, any input would be greatly appreciated.