Basically what CascadingDragon said, Mekanism's Digital Miner does do a scan and harvest every tick. But rather it does a scan, registers everything within the perimeter given to it by you via the configuration GUI, then it starts mining. So in your case, what will happen is if the tree isn't grown yet when you started it, it will not harvest the tree when it matures. If you started the miner on a mature tree, it might (not sure, not used it on trees before) harvest the tree and when done, it will stop. Not paused, it stops since it has completed it's task. So to harvest again, you'll need to go start it up again.
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