After rereading the concept of operations doc from 2011 (which is still relevant today), here is how the OMNY system would work.
It would be account based. Each card or phone tapped on a reader would create an "account" on the server upon first tap, and people can choose to create their own account to register one device.
Fares are calculated on a fare server.
For payment cards without a "product" (passes, money in an account) associated, the fare server would aggregate all the taps every night, calculate the appropriate fare (including transfers, stepups, etc), and then charge the credit or debit card. This will happen for the first phase at the end of the month.
For payment or OMNY cards associated to an account that has one or more associated products, the fare calculation is done in real time. This will come later.
If anyone is interested I can post a link to the PDF. It is quite interesting and shows some real forward thinking.