It is far better to say "Jamie held back his tears at his grandfather's funeral". In the case of "Jamie held his tears back at his grandfather's funeral", I cannot decide whether "back" is an adverb or part of the phrasal verb "hold back".

Personally, both ways seem correct to me. With that being said, I'd also add that I'd probably use the first one more often as it sounds more natural to me. Cheers!

grammatic, hold something or someone back which means that Jamie held his tears back ... is correct

Both are correct, I don't prefer one over the other so you could use either one.