I don't know if Pioneer247 is merely simplifying the notation or he is really mistaken in how he lists the home games in the second round.
Second round home sites are not always predetermined. They could be decided after the results of the first round based on the teams who win that round and thus who has the higher seed in the matchup. (Like for instance, there is no way Utica plays at Cortland, if those two teams should win their first round. That game would be at Utica.)
Another factor many have to consider is each school must put in a bid for each round (due a long time ago), which in part will verify they are even able to host a particular round. Not just because of making sure a school has the proper requirements to host, but also the school has the ice available to host. There have been times where schools play at community rinks, and they have already removed the ice. Or, perhaps the ice was reserved for something else that can't be changed. And we're not talking just game time ice, but guaranteed time for both teams to practice that morning and the day before. Heck, a school may have scheduled a concert in their own rink which simply can't be moved.
So, even a higher seeded team may not get to host for the above reasons.