I think the committee did what they usually do. They mostly ignored conference tournaments especially Sunday (which screwed us), they selected at the bubble based on resume metrics and Q1+Q2 record with a dash of predictives if a team was ranked too high to exclude, and they followed the bracketing principles when seeding.
There's a reason only 1/3 of the brackets on Bracket Matrix had any other Big East teams in. This was the expected outcome for the majority of people, not a shocker. It was a strong bubble, there were ~5 bid thieves, and none of the Big East bubble teams were closer than 2 games under .500 in the first 2 quads. Still, if UNC and Colorado win, Seton Hall is in the field.
Providence had a lot of Q1 wins, but still a losing Q1 record by 3 games (6-9), so it's not as strong a strength as you'd think. They weren't Texas A&M whose Q1 record did offset the rest of the warts. The resume metrics didn't like them because 11 of Providence's 21 wins came in Q4 and they had a combined losing record in the rest of the quads. Where Providence was 10-13 in the first 3 quads (9-12 in first 2), Virginia was 17-10 (10-10 first 2). Thus, the resume metrics like Virginia. The committee likes resume metrics. The committee liked Virginia.
Michigan State had St. John's resume, only better. (Higher predictives, essentially equally crappy Q1 record, but with no bad losses). So if you're going to go beyond the resume metrics and not leave out a high KenPom team, you're going to pick them instead of the Johnnies. The KPI really screwed St. John's.
Seton Hall couldn't get out of their own way. They got blown out by more than 12 points 7 times this year and crapped the bed in the non-conf which killed their (you guessed it) resume metrics. The margin of leaving them out was slim, and the Kadary Richmond "injury" probably cost them a bid by losing that game to Providence at home.