Not exactly how it played out ... though close.
Several elements were in play:
1) It is true that Villanova was Wright's dream job - and his family's. His wife went to Villanova (a cheerleader there, maybe?).
2) The timing of RU reaching agreement with Wright, and Lappas being hired by UMass was also correct.
3) What is NOT mentioned is that Lappas and Wright shared the same lawyer (who acted as each of their agent, I think - but certainly was an important go-between on contractual issues). Wright CERTAINLY knew what was happening with Lappas, even before Wright received RU's final offer - which Wright had verbally agreed to, at a minimum in principle.
4) What is also not mentioned was that Lappas was fired from Villanova after 3 straight post-season performances (records of 21-11 - NCAA, 20-13 - NIT, 18-13 - NIT) - though it is true Villanova wanted NCAA appearances, not NIT appearances. But in 9 years with Nova, Lappas went to the NCAA 4 times, and the NIT 3 times. If RU was not about to hire Wright, Lappas would NOT have been fired - there was literally NO whisper that Lappas was in trouble prior to RU reaching agreement with Wright.
5) What is also not mentioned is that Lappas actually SIGNED a contract with UMass less than 72 hours, or even less than 48 hours, after he was fired by Villanova. It is almost certain that Villanova and the shared lawyer of Lappas and Wright, arranged a quick and soft landing for Lappas in order for Wright to get the Villanova job. This was a superb job by the Villanova AD, but almost certainly partially engineered by Lappas (who was probably told by Nova they were going to fire him in order to prevent RU from getting Wright), Wright and their shared lawyer.
6) In other words, Wright knew he was playing RU and Mulcahy, and his excuse that he wanted to meet with the Chancellor of RU before signed was a convenient after the fact excuse and likely ploy to buy time, not merely a lucky coincidence.
7) Though I have no proof of this, I BELIEVE that Mulcahy had conversations with Wright's lawyer/agent prior to firing Bannon, and legitimately thought he had Wright essentially locked up before he fired Bannon. That actually allowed Wright's "people" more time to work Villanova and the Lappas situation so Wright knew he was not taking a mentor's job, but that his mentor and close friend Lappas landed a good head coaching job before Wright took Lappas' old job.
I am very certain this is how it all went down.