Does the presence of tobacco in the mouth and sleeping before Fajr and waking up after its time invalidate the fast?

It appears your fast is valid, and you should complete it. The substance was applied before dawn, and swallowing — if it occurred — was unintentional due to sleep, which does not invalidate the fast. You acted correctly by discarding the substance, and the fast is not broken unless you intentionally swallowed something from it after waking up. It is obligatory to spit out anything in your mouth if dawn breaks while you are eating. However, the use of this substance is absolutely forbidden, both in Ramadan (definition) and outside of it.