Will Jessie Mueller still be in Waitress in November?

Normal contract length is a year. Now you can figure out the rest

as of pretty recently it's actually only 6 months, I don't know if that was in place when Jessie and cast signed on for Waitress. Either way I'm sure she'll stick around

Don't some contracts start when they begin the tryout?

Nope. Contracts are almost always (in fact, in my experience, always) renegotiated when a show transfers. It's possible if a show transfers with its cast directly that some actors may not want to commit the full standard 12 months, meaning the newly negotiated contracts could be shorter.