In 2016 I bought a set of used winter tires with
aftermarket wheels from the member of this forum. And then right after that I bought my first set of summer tires from Costco - Micheline Pilot Sport 3.
Costco installed Micheline PS3 tires on OEM wheels and reset sensors with their device and it was all good, no warning light. I didn't want to buy OEM Hyundai sensors for the winter tires/wheels so TPMS light was always on in winter, but I didn't care because I didn't want to spend more than $400 American dollars on four original Hyundai sensors for the winter tires.
So I was driving on summer tires from mid April to mid November (no TPMS warning light after swap and reset by Costco device) and on winter tires from mid November to mid April (TPMS light is on). But then in April of 2019, after the swap to summer tires with OEM wheels and reset of sensors at Costco, I got light on after driving for a day. I came back to Costco. They had new device, they reset sensors, but light came back again after driving for a day. I went back to Costco again, they reset sensors again, but light came back on again after a day. So, I decided not to bother with this any more.
So, the cause of TPMS light staying on with winter tires is definitely the
aftermarket sensors, and the cause of light staying on with summer tires mounted on original wheels with original sensors is (I guess) that batteries in those sensors are dead. It may be another reason, but I don't care, the light doesn't bother me. I have a good eye and can visually inspect the tires and manually check the tire pressure.
And remember those good old days when cars didn't have TMPS sensors? How could we drive back then without them?
And what a difference is to drive on summer tires in summer and to drive on winter tires in winter.
I hope I answered your question.