Same thing is happening to my friend and I on my world. My skin ended up being the skin my friend loaded in with, and after he changed his skin it became mine. Additionally, when I tried changing my skin after this, I was forced to only use the 'slim arm' skin, which made my skin have black bars on the arms. I eventually got this ''fixed'' by repeatedly choosing my correct skin base (standard arm), even though it showed as my friend's skin, and adding the 'founder's cape' a few times until it sort of worked. It would be much appreciated if this were to get fixed.
My friends and I are having the same problem, when we load into one another's worlds we get put into our friend's skins and vice versa.