TCU and Boise State were never headed to the Big East together and would never be part of the conference's future at the same time.

TCU was the first school to accept the Big East invite in November 2010. 

Boise State was headed to the MWC.  

The Big East lineup was to be: Pitt, Syracuse, Rutgers, West Virginia, Louisville, Cincinnati, UConn, South Florida, TCU. The Catholic 7 were still part of the conference. The Big East was also looking at further expansion, but no other invitations had been extended. 

Then, in September 2011, the ACC invited Pitt and Syracuse. Then, in October 2011 the Big 12 invited TCU and then West Virginia.

The Big East responded to the Pitt, Syracuse, TCU, and West Virginia defections by inviting 9 schools - Houston, SMU, Memphis, UCF (as full members) and Navy, Air Force, Boise State, BYU and SDSU as football-only members. (This is why I still believe that Boise, SDSU, and Air Force to the AAC is still a viable scenario.) 

7 of the 9 accepted the invitations; BYU and the Big East couldn't come to terms on TV rights and Air Force rejected the invitation.

So, Boise State didn't get the invite until after TCU had already accepted the Big 12 invitation. 

Temple was added in early 2012. 

...but then in mid-2012, Louisville announced its intention to leave for the Big 12 or ACC. And, then in November 2012, the Big Ten invited Rutgers (and Maryland)..and the Big East invited Tulane and ECU (football only). The next day, Louisville accepted the ACC's invite shortly thereafter to back-fill for Maryland. 

A couple of weeks later, the Catholic 7 announced their decision to separate and there were reports that the new Big East TV deal was going to be substantially less than anticipated....which prompted the Boise State departure. 

In early 2013, after Boise and SDSU opted for the MWC, ECU's invitation was upgraded to full membership and Tulsa was the final invitation.