With the two samples, one unchanged and the other going from 9 to 20ppm it appears that something is *not* the same other than the size of the trays. You said that the trays were two different sizes, which means they were not made at the same time. It could be that the one with the higher TDS reading has "something" in its plastic formula that is causing the problem, maybe. Are these new trays that haven't been used for other things? The difference between the TDS measurements of the two different-sized trays is notable, but being such a short-term experiment I would like to see a longer test before I attributed anything to a tray...maybe four or five days of testing...a week wouldn't be too long.
I would definitely do the glass jar test to isolate the mat from all other factors. If the TDS of the water in the jar doesn't rise, then you should be able to rule out the mat material.
It's basic. You have certain parts to this puzzle... trays, mat material, water, pots, grow-mix. The plants themselves should not be a factor. By isolating each part and testing each after at least a couple of days of soaking you should be pointed towards the likely culprit. You need to do the soaking in an inert container of some kind, for example...glass for the mat material, water, and some of the grow mix from a pot. Or, for an empty pot, you could use a rainwater-rinsed plastic bag to soak it in. For the trays simply let some water stand in them. As for the water, test it each time before adding to whatever you're soaking with it.
I would first start with the mat material soaking in a jar. For some reason I'm just suspicious of it. But, with your two different readings from the two trays that makes me scratch my head a bit. Still, though, do a good test with the mat material to rule it in or out.
You've mentioned that you have several types of grow-mix in use at the moment, some from your own repotting and some that plants were planted in when you got them. I take it that the pots with the different grow-mixes share the trays. Rather than taking soil out of the pots to test, I think I would first take a large saucer and top water each plant until you have a good amount of water in the saucer and test the TDS of *each* plant's drain water where it hasn't mixed with other plants' drain water. The TDS will most likely be elevated a bit from all the pots, but if one pot is much higher than the others that could point you towards the problem.
I'm not any kind of pro so take all of this with a grain of salt.
I'm just throwing stuff out there for you to try...if you want to. You have finite pieces to the puzzle...test each one.