Physics Easter Egg from RJ, whom had a degree in Physics.
Unless I'm thinking of another event. He didn't revive a dead tree. He walked through an Orchard, and reversed the DO's taint on the apples. Apples which were immediately rotting as soon as they were ripe.
You should really check out Theoryland's interview database.
Ta'Veren is just part of it, but it's not the only reason events like that happen.
Now reference back to my original comments.
His physical and mental health are both literally tied to the land, in adition to being a Ta'Veren.
It's something unique to Rand, like being a wolf brother is unique to Perrin, or being a lucky gambler is unique to Mat. Rand is literally tied to the land.
His Ta'Veren nature warps the probability of crops spoiling or producing an abundance. It tips the balance of harvested grain spoiling, infested with rats, or remaining pristine.
Similar, Mat's Nature as Ta'Veren warps probability of Odds, and Perrin's ability to sway people to his side. (Rand does both, only with brute Force.)
Ta'Veren nature typically warps probability in the Ta'Veren's favor.
I described his effect on the land as similar to a bubble of evil, because unlike Ta'Veren, a bubble of evil defies probability and creates the impossible.
We have a few things going on here.
1) The land didn't truly start to go bad, until after Rand's injury. It's hard to say, was the DO actively making the land rot? Or was he using Rand's connection to the land, to make the land Rot? Or both?
2) DO's bubbles of evil. I don't know if we know if the DO can control them, or make them do what he wants. But these things caused all kinds of havoc on the land. I'm sure plenty of bubbles caused grain to spontaneously rot.
3) Rand's Ta'Veren nature, leads to weird things happening with the land. Crops suddenly not producing, to crops unnaturally bountiful. Grain spoiling for no reason, rats just devouring. To Grain that got flooded is perfectly fine.
Wherever Rand went, weird things happened like that, and It wasn't always 50/50 good/bad..
4) When Rand was basically reborn on Dragonmount, his physical and mental state were effectively healed.
The land was healed. It's entirely plausible that the land itself started to heal. But the damage was already done.
Where Rand Walked after Dragonmount, the Land around him, almost in a Bubble of Good, did the impossible, and full-stop reversed/healed the damage dealt.
Do we know how much of that was Ta'Veren? How much was this land-connection? Probably not. There was a reason I mentioned Rand and King Arthur.. Whom was also the Fisher King. https://en.wikipedia.org/wiki/Fisher_King