Applied for a job with an academic institution a while back and it's rapidly becoming a huge time sink. Filled out their voluminous online application tool with hundreds of fields to fill, another app with mostly repetitive info to allow background check, now they want super detailed work history with addresses, manager names, etc. This process has already takenat least a couple hours of my time with them asking for increasingly less useful information on making a hiring decision. At what point do you decide to cut your losses with a neurotic potential employer and tell them "no longer interested"? I don't *need* this job and I'm thinking if this is the way they run their organization while recruiting, I'll probably hate my life if I were hired and was constantly being asked for stupid and repetitive information requests.
I worked for a university in the prior decade. Funny how my experience was different. I never filled out an application and there was no background check, as far as I knew. Besides the multiple interviews and my resume, that was it.
Really it is not unreasonable for a prospective employer to contact prior employers about an applicant that they want to make an offer to. If you don't want to give out a manager's name, then give them the phone number of the HR department. Chances are all the information given out will be a validation that you were employed between such and such dates. You can say that the company requires that all requests go through HR.
It may be that the institution may not be a good fit for you. You need to evaluate them as much as they need to evaluate you. Well I guess the answer to your questions depend on how desperate you are or how good the prospective job and benefits are.
On the bright side, you have hopefully saved the information that you provided to the institution. That way you can cut and paste the details for future purposes, as you must have covered all the bases, should similar requests come up again with another prospective employer.