Hello,
I tested on two ipads and an iphone and after you put in a 365 email account address, it does NOT prompt you for work or personal, it goes straight to create an account for me or create a new business organization. We have 25 users in the company using hosted exchange and 365 apps (word, excel etc). I verified this person's exchange info is correct and their teams admin is correct from the portal. It was working it is not any more. Again, no problem when I do the same on a windows PC, it prompts me if I want work or personal and then it gets me to their teams profile.
I called MS tech support and they say they only do limited teams support for iphones or ipads. We made sure the account email address was correct many times, we made sure they didn't have a personal account with the same address, we uninstalled teams on my device, we cleared the teams cache in settings, made sure there were no preregistered accounts.