Okay, I can agree with your second statement. I was only posing the first question to point out the lack of....consistency, that LoZ has with many things.
But my point with it popping out of the ground (although I really agree with your statement) was that the tree may grow at irregular rates depending on the needs of the forest, Hyrule, and the Kokiri. Maybe it's possible that the tree was asked by the light spirits to hold onto the shadow piece, so it grew up faster in order to provide adequate protection. The piece attracted parasites and evil beasts, and the Kokiri had to leave. Being eaten from the inside out, the tree died likely left some seeds to the Kokiri to plant elsewhere.
His father had been asked to guard a precious stone to guard Hyrule, so it would make sense that the son would be asked to guard something similar.
Although that brings up the problem that the Twilit pieces were hidden long ago. Maybe the forest temple in TP is an
older Deku Tree, from a game long before OoT.