Why don't filled doughnuts have compressed dough around the filling? How are doughnuts filled? I thought they were just injected in but that would compress the dough.

The custard jam etc does not appear to be cooked so I assume it is filled after the cooking process.

But the filling does not share space with the dough. (It is in place of rather than being mixed together).

The dough does not seem to be compressed around where the filling is added.

There are no joining marks where the dough could have been removed and replaced with the filling.
Donut dough is extremely fluffy, it's mostly air. The filling takes up a very small volume in the donut. The dough does get squished a bit, but that doesn't look all that different from non-squished dough. 

If you don't believe me, take an unfilled donut, or a roll of fluffier bread, tear out a piece so you can see the inside, then squish the whole roll/donut between your fingers until it's 1-2 cm less tall than without the pressure. That's what compressed yeast dough looks like. 

The baked donuts are simply injected with the already prepared filling from a nozzle, there are no secrets to it.