That might be how it works. Each contender gets to choose follow ups, and if Kasich and Cruz or anyone else is unfriendly to his cause, Trump won’t pick them to such a role.
But far be it for an august agency like NYT to be clear about this. That would raise far less of a brouhaha than leaving it open. There is the muck, we have the rakes.
I'm also sure that the ultimate decision is made by some sort of undefined committee, a group of people. Trump's vote is clear. The others can countermand.