Post-schism. But whether or not they adhered to an Eastern liturgical tradition at the time of their election is unknown.
Historical records show that there were Latin parishes in the Eastern Mediterranean prior to the schism.
I don't doubt the Byzantine Popes celebrated the liturgy in the Latin tradition, as the Roman Pontiffs, but I thought the question was about Eastern (ethnic) Pope rather than Pope who celebrated the liturgy according to an Eastern tradition. :) No big deal. I think it would be awesome to have an Eastern Roman Pontiff again.