They normally have to decide what half of the bracket starts on one day and what the next/
For instance, the 1 side (GO VOLS) of the bracket will start Friday and the 2 side (Kentucky yuk) would start Saturday or visa versa.
That start date would continue through to Omaha. The half of the bracket that started Supers on FRiday the 7th would play day one (June 14) in Omaha. The teams that started Supers on June 8 would have day 2 in Omaha on June 15th.
The Tennessee side of the bracket is 1,4,5, and 8
The Kentucky side is 2,3,6 and 7
1 Tennessee / ECU
8 Florida State / Connecticut or Oklahoma
4 North Carolina or LSU / West Virginia or Grand Canyon
5 Arkansas Kansas State / Virginia
2 Kentucky / Oregon State or UC Irvine
7 Georgia / NC State
3 Texas A&M / UCSB or Oregon
6 Clemson / Oklahoma State or Florida
I'm guessing they'll start the Knoxville Super Region on Saturday as the other half of the bracket hosts are all known even if the visitors are not. The #4 super Region host will not be decided until Monday night when UNC/LSU game is over. I'm pretty sure the winner will be the Super host but the NCAA will make a show of it and make LSU wait until Tues day morning to make WVU or GCU think they have a chance to host.
With these assumptions, I predict Tennessee's first game in Omaha would be Saturday June 15th. I would be surprised if Tennessee as the 1 seed with lots of casual national attention were not the primetime game. Especially if the opponent were Florida State.