It depends what you mean by a country dictated by a Jewish monarch.
Today, the only place you need to separate trumos and maasros is in Israel proper and the Syria that David Hamelech conquered during his reign. See Rambam.
Even if a country today were ruled by a Jewish monarch, that would affect nothing halachically. The only way to require trumos and maasros in a land not in Eretz Yisrael, as specified by the Rambam, is for it to be conquered by a legitimate Jewish king or Navi [neither of which exist today] with the consent of the Jewish nation.