Dream job but the hiring manager was kind of rude - is this a red flag?

I went to the final stage interview for my supposed dream job. For the most part the interview went well. It got to the part where I asked the hiring manager questions, I asked a number of them then asked “how would you describe yourself as a manager and how do you think your team would describe you?”. The hiring manager asked me “do you think this is relevant to our conversation?”... floored.

I proceeded to justify my question explaining it was important for me to get an understanding of their management style and I asked how the team would describe him/her as I heard great things about them etc etc... the hiring manager then said they was only teasing after they saw the panic on my face and laughed but I don’t think they was at all. In fact the hiring manage made a throw away comment about it sounded like I was interviewing him/her instead of it being the other way around.

I have been quite reluctant about this position due to the flakiness of the hiring manager sticking to agreed interview time, my pay would remain the same etc etc. Isn’t this odd?

I am really keen to leave my current job but I will not leave out of desperation this time around. Don’t get be wrong the hiring manager was lovely overall but that awkward moment is really a red flag for me.

Am I over thinking it?