Since I don't see that anyone has answered your question, I will try.
A Chrysler scan tool, on your 2016, will only tell you how many starts since a code 1st appeared or was cleared.
That's only if the code wasn't permanently cleared in the PCM/BCM.
It doesn't display a date. So for example, if a code sets, it'll display that the code set at 24 starts since fault.
I worked in a used car dealer for a couple of years, I'm going to tell you, most of those aftermarket warranty company's won't pay for much.
Transmission and engines usually "covered only if damaged by the failure of an internal lubricated part". That almost always meant that if you have a electronic part creating a issue, they won't cover it.
The best advice I can give you is to take it to a place like Cottman or AAMCO, pay to have it fixed, then demand a refund for the warranty. I wouldn't be hesitant to file a lawsuit against the dealer for misrepresenting the warranty they sold.