Does filling in the W-8BEN form Payoneer asks for mean I pay tax in Turkey?

No, that form has nothing to do with Turkey. The W-8BEN tells the party making the payment that you are not a United States resident, so that withholding there is applied correctly. Filling it in neither creates nor removes an obligation in Turkey. Tax here looks at whether the earnings arose in Turkey and at your own registration; the form does not enter that calculation.