Get the offer in writing.

Flight schools have a way of baiting newbies into jobs with the "promise" of transitioning to turbine equipment. I don't know what school you speak of or how much time you have now/would fly there, but I'd imagine to instruct in a King Air you'd need an ATP at the very least, and the Citation...I'd guess AT LEAST 2500TT. Who has a friggin' Citation available for dual given anyway???

Either way, follow your gut instinct. Upgrading at TSA will take a while, but if you want an airline career you can work there for a year or less than get hired at most any other regional you'd want to go.