In a former life I was involved with this. Unless some rules have changed in the past few years it pretty much went like this:
1) when selected for tournament usually the director of operations for the team would receive an email from ncaa about travel party, itineraries, hotel, travel.
2) if travel was under 350 miles the travel was by bus, if over then by charter flight paid for by NCAA. Also about this- if the team was under the 350 miles they could charter but the extra cost associated with flight would be paid for by the school.
3) fly/bus to destination usually day before mandatory practice/press conference
4) play game, off day practice/press, play game
5) after a loss or advance to sweet 16 return travel to campus would mostly be based on time of your final game- day games are definitely traveling home same day, evening games could go either way based on available planes/busses, late games typically will fly out next day when planes/busses are available.
For flights NCAA uses all different companies for flights- Southwest, Sun Country, Miami Air, Orange Air (now defunct) are a few names that I was familiar with in the NCAA charter flight world.
The Colorado State situation is super weird- almost as if the NCAA emails were sent to the spam folder.
