I have a potential postdoc abroad, administered by a foundation. The foundation pays half our salaries, and the other half is covered by a faculty sponsor. Two professors are splitting my cost. Earlier this week, I visited the potential postdoc on my way back from a conference abroad, my first conference outside the US.
The justification for postdoc positions is to offer continued training, such as specialization or professional development, prior to a permanent job. Since postdocs are a halfway position between graduate school and a "real" job, they're paid, but usually significantly less than faculty. Despite the intention for postdocs to be engaged in training and professional development, sometimes postdocs turn out just to be a labor source for faculty in ways which do not serve their professional interests.
The official postdoc regulations at Potential Postdoc University say that postdocs are not expected to do any specific work in return for their funding. A philosopher friend of mine took this postdoc several years back, and all he did was work in the library on his own projects. Since I suspect that there's very little research assistance that his sponsoring philosophy professor could ask from him, there was little risk that he would be used as a labor source. In many fields, though, sponsors can get some return on their money by asking their postdoc to contribute to their existing projects. Since the sponsor believes that the projects are useful for their own career, it's easy to justify that any productive work is professional development for their advisee.
I met with my two potential advisors separately, and they illustrated this tension perfectly. The first started the meeting by saying, "Here are the two projects you'll be working on." and then describing the projects, neither of which was clearly related to my past research and were arguably not even in my field, so wouldn't improve my marketability. Since he does do work in my field, it should be possible to find a project that would help both of us, but we didn't get that far in discussion.
The second asked me what I would like to do, what would help me in my career, and whether I'd later be interested in applying for a faculty job there; and she suggested some projects which were definitely in my field, and said others were possible using existing resources.
The two approaches could not be more different. One thinks only about his own needs, and forces the postdoc to start a new advising relationship in an adversarial way by objecting to her marching orders, and if necessary pointing to the university's postdoc regulations. After these negotiations, either everything would work out, or the relationship would be poisoned and the advisor would refuse to renew the funding. The other clearly wants to do her own projects, but also wants to make sure that the postdoc's larger professional development is served by the work.