Yeah, I went from OEM wheels+tires to winter wheels+tires about a month ago, and the TPMS warning light will activate within a few moments of putting the car in motion, if not sooner, and stay lit. It's basically never not-lit, except maybe when I first start it next to my stacked OEM wheels+tires+TPMS sensors.
You should also be able to tell because the TPMS stems are hard plastic and kinda short, aftermarket stems would generally be flexible rubber and a bit longer. I suppose perhaps your dealer was looking for a way to 'blame aftermarket' and not-help you with their product. Awesome. :/
Before I removed my OEM wheels+tires+TPMS sensors for the winter, I did notice that on cold mornings, it would start out lit, but then go out later in my 44 mile commute. Does this describe your experience? So, basically, when thinking about tires, there are two pressures to keep in mind: cold pressure, which is the pressure of the tire before it has been in motion, say, when you go out to start the car each morning. And then warm pressure, which is (as you'd expect) the pressure the tires reach when they've been rolling at speed a while and warm up. When you open the driver-side door and look at the factory sticker that lists tire sizes and pressures, they are referring to 'cold pressure.' If, for example, you drove to the gas station and checked the pressure there, if you filled to this 'cold pressure' while warm, you'd in fact be making your cold pressure be too low, effectively not meeting the recommended minimum safety pressure, causing undue wear+tear, a slight loss of MPGs at fill-up, etc.
The rule of thumb I've heard is that for every 10'F below the tire air fill-up temperature, you lose 1 PSI. So, even if you are careful to check and add air when the tires are truely at their cold pressure condition, if the temperature drops, say, 40'F from that day, you'll be up to 4 PSI low. I've also heard that the Mazda TPMS sensors will alert to 'low pressure' at 20% below their set/calibrated pressure, which I would assume is about 32 PSI from the factory/dealer. I guess that'd be about 26 PSI, but it could even be higher.
With winter cold fronts coming through, it's very plausible that you might be starting at a cold pressure below the door plate's minimum recommendation, low enough to trip the TPMS 'low pressure' alert, but once your tires have been rolling, they heat up some amount. A 20-30'F difference might be enough to bring them back up 2-3 PSI and put them back within the TPMS sensor's programmed acceptable range.
One other thing to keep in mind is that the 10'F rule may not apply if your tire dealer gave you a nitrogen gas fill instead of compressed air. I have read pure nitrogen gas is less susceptible to PSI changes with temperature. Either way, either by giving you nitrogen gas filled tires, and/or just giving you a proper cold pressure, your tire dealer probably corrected what was an ongoing slightly-low pressure. That's my guess, anyway!
