The Chiyuv of accepting Tosafos Shabbos and the validity of the Shabbos that you accepted are two separate things.
On Motzai Shabbos, though, I remember aa Tosafos that says you won’t be Chayav for doing a Melacha before Havdala. There is a Chiyuv to be Mavdil but you can’t be Chayav until then.
The interesting is though, that the Poskim discuss telling someone who was already Mavdil to do a Melacha before you were Mavdil, without mentioning this Tosafos.