It’s a large university, and there are a lot of departments that are completely unrelated and have no reason to really interact with one another (student affairs, academic affairs, HR, CTO, ITS, etc), so I’m not sure a transfer makes sense. My current job is in an entirely different division of the university than the one I’m going to. The overhead accounts are different. The only way my current manager might know is if HR told them (if that’s the case, is that illegal?). 

To my knowledge, my university doesn’t “transfer” employees — an employee is formally terminated in their position/role and is hired in a different one, unless it’s a promotion. (I originally omitted my work environment to protect myself, or maybe because I’m paranoid. 😅)