Oh no
I feel your pain.
We had allotments in Edinburgh for about 10 years and they were infested with NZ flatworms, to the extent that there were no earthworms such as Lumbricus sp left!
I'm upset too as it was me who recommended Cheviot to you. I also bought two potted trees from them and didn't think to search for flatworms or their eggs. Too late now as they've been in for 2 years
So, what to do about them. My knowledge is not exactly current, but 25 years ago the researchers at the Dept of Zoology, Edinburgh were finding that beetles such as the Violet Ground Beetle, were great predators of flatworms. I think the VG beetles just happened to be the ones that were available to the students at the time and I suspect that many other of the big beetles will predate flatworms. So, encourage any and every beetle you can. I dimly remember that they found blackbirds would eat them, although as they tend to hide somewhere damp I don't see how. Research must have come on since then, perhaps at the agricultural places (the one near Maybury?) as well as Unis, but I'm afraid I no longer have access.
At the time I approached what is now 'Garden Organic'(of the ungrammatical name) and had a very snotty reply saying that as it was only a localised Scottish problem they were not remotely interested and had far more important things to do. I think that has come back to bite them in the bum!
I'll have a delve around to see if my pathetic computer skills can come up with any further info.
If you ever get to the state we were at at the Saughton allotments, of no earth worms, then there are ways of living without them but with flatworms.
People had taken to building their compost heaps up off the ground so that at least the tiger worms could work away, but on a smallholding level that isn't really practical. Perhaps surrounding them with pond grade thick polythene would help.
I think you will be ok inside your tunnel as if it's anything like ours then the soil dries right out in winter and they really don't like that.
You would find that your usual way of perhaps adding mulch onto the top of your beds and leaving it to the earthworms to work in won't work. I would find that manure I had put in potato trenches was still in exactly the same place when I dug them back up. So any soil additives have to be thoroughly mixed in, and you have to dig ie not 'no-dig' to keep the soil aerated.
Beyond those measures, and trapping them as Doganjo has said, there's not a lot you can do.
At the moment, as your trees are newly planted, any released flatworms are unlikely to have moved too far away. I would suggest putting tiles, or bits of polythene flat to the soil and checking every day. The eggs are like blackcurrants, often found between the pot and the roots and if any of those were present, they might have dropped down to the soil and be hatching.
Of course remember not to bring any of that soil anywhere near the rest of the holding, and check your boots and tools if you've been working there.
btw we managed not to bring any flatworms with us at all when we left our allotments behind and moved to our smallholding. We washed absolutely everything, including some paving slabs in the river and the only plant material we brought was well washed comfrey roots, so if you're careful you can deal with them.