Employment in Netherlands and Germany. How to work on income tax?

Hello,

I would like to ask some advice on income tax in two countries.

My partner is spanish has a full time job in the netherlands. He is living in the Netherlands with me. Some part time job opportunity (remote) came up from Germany and he took it.

Since mid 2020 he's been working two jobs from two different country
1. full time in Netherlands
2. part time in Germany (a different company from the netherlands one)

From my research and understanding he has to pay full income tax in the country he is residing in which is the Netherlands. And then he has to ask his german employer for some paperwork and some tax return from Germany which is then paid in the Netherlands (the country he is residing). Is this correct?

I would also like to ask if anyone know which services we should go to, to help figure this out.
Any links for information or services will be really appreciated !

Thanks!