3rd parties suck ass. My fiance got rear-ended by a FED EX truck, and they had a 3rd party do the risk managment/claim (not an insurance company) and they fucking suck.
I am retired but I could write a fucking book about job hunting experience. And another about actually getting the job. When I first retired I thought I might take an occasional short term gig for extra money but I am so damn glad to be done with them. I still get calls from recruiters and as Nancy Reagan out it just say no.
It wasn't handled at all professionally. I would have been pissed and let them know it after that grade school exchange on their part. Best consider yourself to have dodged a bullet by not working for an outfit like that.