Regardless of your Estonian e-Resident status, you must always pay personal taxes in the country in which you are a tax resident. For a regular employee salary, you will not pay tax in Estonia as a non-resident. Read more here.
Estonian companies need to withhold income tax from all the dividend and director fee payments and social tax from all director fees.
If your company is registered for VAT in Estonia, you also need to settle your VAT account with the Estonian Tax and Customs Board every month.