I'm going to try to get the official word from Tesla or Impark (which owns the lot) but I strongly suspect that you do not have to pay for parking while using the chargers.
As others have noted, this is a pay-by-plate lot. There's no gate at the entry or exit, you're just expected to go to a pay station and pay for your time (or use Hangtag). The lot is periodically patrolled to ensure compliance. So, no need to have a "paid" ticket to exit. That said ...
People who are not charging cannot park in these spots; they're set up more like gas station aisles than like regular parking spaces (unlike some parking spots on the first level, which are used for Modo and Zip cars, including EVs.) These were specially modified by & for Tesla, which strongly suggests that Tesla has a long-term parking lease on them.
Moreover, even Tesla owners can't park there when they're not actively charging. Tesla dings you for leaving your car connected after the charge is complete, and that cost is 50¢ per minute ... a lot more than the normal parking fee at that lot.
So, my guess: Tesla has a lease on those spots, they're only for Tesla drivers, and only for their use while actively charging (or you pay a lot more).
When I get confirmation on this I'll post it.