I have notice that the tours do not include the admission fee to both.
Not sure I want to wait in line to pay for both attractions along with
everyone else on the tour.
What tours are you looking at? If you're on an escorted tour, with a guide, you will do any waiting that's necessary to keep the group together. How tickets are collected, how much waiting is involved, etc. depends on individual tour operations as there's no single company which does these.
We did Pompeii on our own and didn't experience much of a queue at all but were there before the opening hour in the fall.
Personally? I wouldn't do both Pompeii and Vesuvius from Sorrento in a single day but that's just me. In fact, we skipped Vesuvius altogether as you can see it clearly from Pompeii, just as the unfortunates who perished in its eruptions did.