The 360 version was planned from the beginning and was greenlit after a technical test early in development. Nixxes weren't alone in the dark on this game. Crystal was limited to making animation/AI/core features that could run on both gens from the start as per publisher plans for cross gen. It's delusional to think that they would give Nixxes the small porting budget but have no scope required at Crystal to support the 360 port. It would be a huge waste of money if Crystal had been free to truly make a bunch of current gen only features that would break running on last gen, as then they would have wasted money on Nixxes trying anything at all.
That would be like spending a few hundred thousand on Arkham Knight getting a last gen port, only to learn the stupid way that the Batmobile couldn't happen on last gen due to all the streaming/AI/etc.
So no, Rise of the Tomb Raider on 360 was not made based on a totally current gen code that had cross gen consideration. It was totally cross gen and the studios absolutely would have worked knowing the need for the last gen release and that to blow it kills significant publisher money.