That you can be sure of, and I don’t know whose “Slavic” tradition this is, but it sure as hell is not Polish tradition.

Polish father and non-Polish mother produces child that is half-Polish and half-whatever else and is considered so in Poland. I am sure it is same in Russia (hence designations for “Rossiyanin” and “Rusak” in Russia to separate natives from foreigners, just like for example in France you have “Francais” and “Gallois”) and I can’t imagine it being different in other Slavic countries, including Serbia.