The labor taxes on salary are paid in the country where the work gets done.

The income tax for the board member fees is paid to the country, where the company has been registered, but the labor taxes to the country, where the person's social insurance lies (usually it´s the person´s country of residence and it´s the same in all of the EU countries).

If the person moves to Estonia, the labor tax is also paid to Estonia (also called a social tax in Estonia).