If the release of this water was as stupid as the articles linked here suggest, his administration is responsible, no matter how this occurred. Obviously. Trump's level of culpability in the whole thing can never be zero, but it's worth asking how exactly this happened.
We don't expect our Presidents to order certain dams to be opened at certain times, etc. without others weighing in and advising, do we? Now, is it possible, Trump said "I don't care, just do it. Open those dams no matter what, I know what's best?" Yes, yes it is. But I think it's important to know if it is that or some admin miscommunication, foul up down the chain, etc.
As for him claiming credit, Trump would boast about his morning stool if he thought it would make him seem successful. Doesn't mean we have to pay it much credence.