That depends on what you mean by "primary". CTRMA (Austin, TX) and NTTA
(Dallas/Ft Worth, TX) give discounts for using a transponder, but those
without are simply billed by mail at the cash rate. As long as the bill
is paid on time, there are no fines.

how does all this work with rental cars?

The rental car company bills your credit card when the charge arrives,
and sends you an e-mail saying that they did it.

R's,
John