Leaving a digital miner in the Nether or a Mystcraft dimension will result in the miner resetting when exiting that dimension - even with the presence of a chunkloader.

You should use for example Dimesional Anchor from Immibis' mods.

It will be good idea to add a chunk loader to Digital Miner or a chunk loader to Mek.

Well, this doesn't happen to me, I have no issues with chunkloading digital miners in the nether.
EDIT: It just started happening to me, when I leave the nether, despite having a world anchor next to the miner. When I get back the total blocks to mine will be 0 requiring me to hit the rest and start buttons again.

As I said in the OP, I already have the miner chunkloaded.

I think the act of switching dimensions affects its state somehow.

This is actually not an issue - the reason why the miner resets is because the chunks it is trying to mine are actually unloaded. The way to fix this is to introduce a chunkload upgrade for the miner, which I plan to do.