Sprint models (variants) are. by definition, NOT T-Mobile variants. It's impossible for a device to be bothThe OP is pretty unclear since it talks about Sprint users (as in, on a Sprint line). I want to buy a new device presumably from a T-Mobile store under a Sprint account, but use it on a T-Mobile line.
Specifically, "Can be bought 3rd party but must be the T-Mobile variant and on the T-Mobile network.". Sprint models are T-Mobile variants, and will be on the T-Mobile network. Hence the question.