Here's my experiences so far:

Personal car with NY EZ-Pass registered to my account - I drove in via the Lincoln after peak hours so was charged the $2.25 overnight fee with no crossing credit. The toll posted about two days after I incurred it.

Hertz Rental Cars - Despite trying to use Toll By Mail as advised by the MTA, the charges aren't captured in time before it's sent to PlatePass so you are forced to pay the convenience fee ($5) and a reduced flat congestion fee of $9 (no overnight, and no crossing credit) for an all-in of $14, $0.50 more than the cash rate of $13.50.

I have an Avis rental charge pending, so will see how that ends up getting charged.