From a support ticket reply from @mwestphal
With unstructured grids, such as a single vtu file, the distribution of data is not free and has to be done explicitly.
One way to do that is to use the D3 filter, like this :
Run pvserver in parallel
Run paraview, connect to pvserver
Open your .vtu file, Apply, it is not distributed
Add a D3 filter, Apply (can take some time) , dataset is now distributed
Save as a .pvtu file
Reopening this .pvtu file on a parallel paraview will give you a (statically) distributed dataset, while working with D3 directly will give you a dynamically distributed dataset but take more time each time you want to distribute your dataset.