Some seedlings you put into the ground with as little root disturbance as possible. Sometimes it's plant specific. The label (or online charts) will tell you if it's better to start seed directly in the ground.) If the root ball is tangled and in a rootbound mess, you can safely work the outer roots free. Cutting them isn't harmful, it stimulates more root growth.

I think your problem may be simply transplant shock. It takes a few days to adjust if it's sunny out. Some of us wait for a cloudy day to transplant, or at least in the late afternoon. You may have to put some shade around the plants till they adjust. Don't drown them, but keep them consistently moist.

If the rootball is that tangled, the plant may be too old and rootbound for successful transplanting.

It is plant specific to a certain extent and it depends on how much root there is whether you want to try to spread the roots out. Plants that are small and not root bound don't need their roots spread out, and plants that don't have their roots messed with have less transplant shock. But sometimes you get transplants that are root bound and if those roots aren't spread a bit the plant likely will never thrive. But once you do that, they need extra attention paid to keep the roots moist at all times while they recover from their "surgery". And even with that done, a really badly root bound plant may remain stunted. Good luck can be had with that method on plants that are just becoming root bound, though. All transplants need a bit of extra water while they send their roots downward, but non-rootbound ones don't tend to need the TLC for as long after tranplanting as do the root bound ones.