@Maria Sophia I have also purchased several properties in the Wayne County Tax Auction. While many commenters suggest there is a 6-month redemption period, that is only true for Mortgage Foreclosures NOT Tax Foreclosures. You could have this person out in less than 6 weeks.
I agree with most of the other comments....Get an attorney! If you want someone that just does evictions try James Abbot. For general real estate stuff (including evictions) I have worked with Harry Kalogerakos, and Raymond DeBates, both are good, reputable attorneys.
Honestly, your best bet is to approach the previous owner and explain the situation to them and negotiate a move-out deal. I have 4 properties that came with occupants, two of them are previous owners. In one case, I'm selling the property back to the homeowner on land contract. The other person, I have given a grace period to move out (where they pay $200 /mo. in rent and if all payments are made on time, I give them their rent back by an agreed upon move out date...like cash for keys with more accountability). My guess is that your property management company approached the homeowner without much empathy, and the occupant is right to be skeptical as many people don't realize they've lost the home. It took me a letter, two phone calls, an in person meeting, and over an hour of explanation to get one of the previous homeowners up to speed. She couldn't understand why she didn't get notice about the actual auction sale....and I said "You did, you got foreclosure notices, and once they issued a default judgement, the County doesn't care anymore."
Just remember, this is bad situation for the previous homeowner, they likely have very little money and may not have a place to move to. Tread lightly, and you will be far better off.
Good Luck!