Online, or through the Ohio ticket office? My synapses may be disjointed, but I seem to recall being automatically charged for round two tics in '10. Could be wrong, though.
If you buy your tickets from Ticketmaster, they are generally sold as a "strip" or weekend set. So you do get all games at the site for the weekend. For example, a "strip" for last weekend would have included three sessions.
Session 1: Cincy/Texas and Florida State/St Bonnie
Session 2: Ohio/Michigan and Temple/USF
Session 3: Ohio/USF and Cincy/FSU
If you bought through the school (Ohio)...you were ONLY sold Session 2. ONLY if Ohio won, were you billed for Session 3. You only paid for tickets to sessions Ohio played in. This was the same for 2010.
For this weekend, there are two sessions:
Session 1: Ohio/UNC and NCST/Kansas
Session 2: Winners play for Final Four trip
This time, we are required to buy both sessions upfront. So we have tickets for Sunday even if Ohio does not advance. However, it sounds like we cannot pickup Session 2 tickets until 90 minutes before the Sunday game. That limits opportunity to unload the tickets should we lose Friday night and want to return home. We're in the Sweet Sixteen, so no complaints. But would be nice to get Sunday's tickets on Friday so we have options.