How to deal with hostility from administrators when starting a new postdoc position?
Is this usual behavior
Short answer: no.
Longer answer: I have heard many stories of bad workplaces, both in academia and beyond. Even at good workplaces one occasionally encounters weird, rude, and borderline exploitative practices and staff/employer attitudes. So perhaps it’s not entirely accurate to say it’s not usual. But by and large, the situation that you describe does not sound good or normal. Self-respecting, respectable US institutions will generally go to great lengths to make their postdocs feel welcome, and will have an orderly, transparent hiring and onboarding process, clear policies, and staff that will communicate those policies to you upon request (even if not always in the most friendly or efficient manner). That’s quite a contrast with what you are describing.
and how could I deal with this most constructively?
Since you bring your own scholarship and generally sound like you are an attractive hire (and someone who has the self-confidence to not be shy about being one) I would guess that you have a fair amount of leverage in this situation, and will assume in this answer that that is the case - specifically, that you have a reasonable likelihood of finding alternate employment quickly if the current offer does not pan out. You need to put that leverage to use. The key is to make the professor/mentor-to-be aware that there is a minimum level of treatment that you are expecting from him and his department, and that should he fail to offer you credible assurance that you will be receiving that minimum, you have other options and will go elsewhere.
To put it bluntly (although in your communication with the professor you will want to be less blunt), you need to make a credible threat about withdrawing your acceptance of the offer to join the professor’s lab, assuming you’ve already accepted, or about not accepting if you haven’t yet.
In preparation for bringing this up, there are two crucial pieces of information you will need to know:
What are your options? Do you have other places you could quickly arrange to give you offers? Given that you have your own scholarship, I am hoping the answer is yes. But do your homework and explore this at least informally, by sending out feeler emails etc.
What are your minimum expectations from the current professor and his lab? That’s a personal question you’ll have to ask yourself and answer - it may include things like health benefits, a written contract or reference to a set of institutional policies governing your type of position, a conversion of the “visiting postdoc” to a title more commensurate with your qualifications, or similar things.
Once you know the answer to the above questions, ask to have a video meeting with the professor and politely bring up your concerns. Be tactful, and make sure to mention all the positive things that make you want to join his lab rather than someone else’s, but also make it clear to him that your concerns are serious enough that you can and likely will withdraw your agreement to join his lab if he does not take them seriously.
I mentioned the threat to bail out needs to be credible. That means it would be good to mention any specific facts at your disposal to make it seem like you have the ability to act on the threat (again, I am using blunt language - I trust that you can phrase it more diplomatically in the actual conversation). For example, you can mention names of specific places where you have a pending offer or promise of one, or at least adopt an attitude that signals your confidence that you can get another offer easily because you have your own funding.
Finally, part of making the threat credible is that you need to be mentally willing to act on it in the scenario where the conditions you are setting are not met. If you think you’re not willing, the approach I am proposing may not be right for you.
Good luck! I hope things work out. But cover your bases and be prepared for the possibility they may not. Honestly, this behavior does not sound normal, and should not (in an ideal world at least) be an acceptable way to treat people.
I'm not sure why you are considering this "offer". You've given a lot of downsides that could easily lead to future pain and suffering. But other than a weak endorsement in your first paragraph, you haven't really given any positive aspects to this position.
If you have any other offer(s) with better conditions, you should probably consider them first. If it is this or nothing at all, then be very wary if you take it. The professor in question can probably help somewhat.
I'll note that some of the restrictions given by the administration are probably the result of laws that must be followed, since the position is not a standard one. If you aren't a regular employee, then you don't have the protections (or requirements) that regular employees have.
Currently, I am in a similar situation (working since 12 months as a postdoc in the U.S. with a scholarship that covers 24 months from the "NIH" of my home country). Similar to what you described, I came expecting to be a regular postdoc based on the prior communication with the PI.
Personal situation: Upon my arrival, I quickly realized that my PI does not support me or project in any relevant manner and that I am essentially a visiting scholar working on a line of research that is as of today not really of interest to my PI. In the beginning, I was super motivated and provided weekly detailed “Objectives and Key Results” (OKRs) during our meetings. I would recommend you to give it at least a try. Nevertheless, over time I had to somewhat realize that the meetings should be kept as slender as possible, given that the technical/research feedback is limited either way. I decided to stay and I do not regret it too much. The PI is overall a supportive and respectful leader. While I have to apply for computing resources (applying to Google Cloud credits) and organize data (i.e., setting up MTAs with other institutions) myself, the PI allows me to do so freely. Nevertheless, I keep him always in the loop. I am still thightly conntected to institutions in my home country - i.e., getting data is not a significant bottleneck for me. The institution provides a strong halo effect and is an interesting place to be for me, irrespective of my output.
Thus, the following factors are in my view important to consider:
Do you expect your PI to be supportive even if you work somewhat like an independent collaborator on your own projects?
Is it possible to obtain data in chemistry independently or are you very dependent on the group?
Is the institution/environment exciting enough to justify some degree of a diminished research output?
If the answer to all 3 questions above is not "yes", I would recommend to leave. While you may want to try to talk it through with your supervisor, do not expect that you will be able to change too much about the supervision style.