If it uses the same bands (frequencies) as TMO, then the phone will work provided that it is unlocked. If the phone is locked, it will not operate with a different carrier's SIM card.
It's probably based on the agreement between the MVNO Ultra (who I've never heard of, but that means nothing) and T-Mobile.
I can tell you that Walmart Family Mobile plans (powered by T-Mobile) do let locked T-Mobile phones on their network.
I think that's the advantage of StraightTalk as well -- you don't need to be unlocked if you pick the carrier of the phone you have (keyword is think)
So, there's a good chance that if Ultra is a T-Mobile MVNO you don't need it unlocked. Easiest test? Find someone with a T-Mobile branded phone that's not unlocked (if they don't understand then it's probably not unlocked) and pup your Ultra SIM in it. You may even be able to hop into a T-Mobile store and borrow an employee's device to test it. Especially if you are intent on purchasing a device, they'll probably be more helpful.