Yellow NM cable from the major brands (e.g. Romex) is #12. White NM cable is #14 and, because of the code rule requiring that small wire sizes be increased by 1, it wouldn't be permissible to connect a known 20A load using #14.
An actual 20A outlet will typically not have the spring-loaded "backwire" or "stab" terminals common to 15A devices. There may be holes on the back but they are clamped down by turning a screw. These are fine. I agree that spring-loaded backstab terminals are to be avoided unless working in a very tight existing box where the saving in space from wiring through the device (using both terminals) is necessary.
Anyway, your electrician didn't upsize the wire for the long run, you've got the wire size required by code. Do you know what your starting voltage is before you begin to charge? You may have to be pretty quick to see it with only 12A of ramp-up but it'll be displayed on the instrument cluster at the very beginning of the charge cycle.
I don't know if the threshold used at low amperages differs, but the car will usually tolerate about a 10% voltage drop before limiting current. That suggests you would have had to drop to that 110V you're seeing from an initial (no load) voltage somewhere above 120 -- is that the case?
Do you have another large load on the subpanel (say, a washer or dryer) which might have kicked in at some point just as the car was starting to charge, making it think the wiring at this location was unreliable? If so, restarting the car is likely to help.
