I should imagine it works the same as anywhere: you have cleared the chat outside of the required time to "delete" that message for both of you, so it's only going to clear for YOU, not for both of you.
However, with that said, as a regular user, I don't have a clear messages option, so maybe it does clear for both of you? Maybe it clears content you sent but not regular messages? Definitely ask to be sure exactly. I would always assume it's the former of all of this though and it only clears the entire chat for you.
If you do find out, let us know if you can please, it's always good to know a bit more