It shouldn't grow to the second stage, because in the beta changelog, it said that they had a known issue of in game ticks not working.
"Known Issues:
Game ticks don't affect blocks changing states – this issue means that crops will not grow without bone meal, and grass will not spread etc. – we aim to have this resolved for the next beta update! "
Just to restate this, Jeremy Wilson said this, but it is kind of buried, but it can be fixed by throwing the item out (via q, holding the item for mobile, etc.)
I almost died recording a drowned with a fishing rod trident only to find this bug report. lol