OT Coin Toss = 49'ers Demise?

This became a new rule this year for postseason games. As the ref explained at midfield they were starting a new game with both teams getting at least one possession unless there was a defensive score on a turnover on the first teams possession. Had the first overtime period expired they would have reversed field direction and started a new quarter. The game would not have ended in a tie. Once both teams had a possession they would have played until one of the two teams scored no matter how long it took.
As I understand it, that's not actually correct. The entirety of the OT period is treated like the end of the half or end of regulation. They would start the 2nd OT exactly like the first OT except I think they switch to whoever lost the coin flip in the first OT. Maybe the rules change that, but I'm pretty sure that's how it was previously.