They count for sure in adding up your payroll. I don't know if the money gets paid when the player is in the minors. Check the salary report under the front office tab.
My work around is to limit 40 man roster spots to useful call-ups when I can. It's not always possible. If you need to add a bunch of filler suspects to ST just waive and DFA them after the last ST game. Most AI teams will have full rosters anyway so it's unlikely they will be claimed. If any are good enough to attract attention then you should have to make the choice to pay them or lose them.
This is a cheat.
You can do the same thing after the rule 5 draft.
OOTP badly needs a separate ST roster. If it can be done for the playoffs (not well), it should be doable for ST.