It shouldn't change anything in the immediate future. The capital expenditure to build the attraction almost mandates that the contract has a lifespan built into it. The fact that when Disney, aka competitor right down the street, acquired Marvel, Super Hero island didn't shut down or retheme. Or when Disney acquired Fox Springfield didn't go away and T2 didn't shut down (immidately) should be a good indication for how the contract would most likely be set up.
However, any new arrangement, particularly with any direct competitors, might trigger opt out clauses or mutual interest in abandoning the property leading to changes. But anything like that, for an attraction as new as Bourne, should be YEARS away.