I have a Focus, 2 years old, probably a similar system to the Fiesta. I bought a spare set of wheels with winter tyres and TMPS sensors, 2 years ago. For the first winter, I couldn’t find out how to get the car to recognise the sensors, and I had the warning light on all the time, and it beeped occasionally. There are various reports on the web that you deflate the tyre to wake it up, or hang a magnet round the valve – neither worked for me.
I then bought an ATEQ VT15 actuation tool (£135 on eBay) – each time I swap the wheels from summer to winter or vice versa, I do a sequence with the ignition key and the brake pedal, then go to each wheel in turn and point the VT15 at the sensor, which wakes it up and the car recognises it.
Something to watch for is the sensors on the aftermarket wheels have metal valve stems, not rubber. After the second summer, two of the tyres had gone flat in storage, and I found leaks round the valve stem. Had to get two new valve stems, £90, not happy. If you get metal stems, I suggest greasing the outside of the stem to keep the road salt off; I think it was corrosion that did for them.
I may be wrong but I think it’s an MoT fail if the car is showing an error on the TPMS, so you need sensors in and recognised when it goes for the test.