I've been a supervisor and manager for a very long time (mostly military but now private).
I recommend you ask to discuss expectations from your current supervisor. Find out what he/she wants. If that doesn't match what you expect then discuss them. You should not be expected to work that much and in those conditions if it is not the company norm.
In my experience, managers respect those who bring up problems and try to work them out more than those who are 'Yes, people'.
Good luck with the new job.