>Over here the car would be marked on first round, checked again after max time expires and get a ticket even if the meter was filled up again without moving the car.

Sounds like it's different over there.

My expectation here is that, unless otherwise posted there is no maximum time period you can park. Putting coins in the meter buys you parking rights for a certain period of time. The more coins you put in, the longer that time period becomes. You can add additional length at any time merely by putting in additional coins.