See question 4037 above regarding ashes of gentile deceased person stored in a home, and that Cohanim don’t have to be concerned. Why should they not be concerned that the ashes belong to a Jewish person, since it is not uncommon for irreligious people to also cremate their deceased close relatives (also to save cost) and maintain them with them. Then the prohibition of Tuma for Cohanim should apply?

Horav Shlomo Miller Shlit’a opinion is that since the bodies were cremated and the burnt bones were crushed and ground into a powder, even if they belonged to Jewish individuals, those ashes don’t carry a Tuma that prohibits Cohanim to be under the same roof. See also Mareh Habozok (5: 102) that deals with the question of entering a monument Ohel Izkor that honors the ashes of Kedoshim and martyrs and victims of the Second World War or other victims, and permits the Cohanim to enter since the burnt bones are totally ashes. See also Pischei Teshuva (Y.D. 369: 2) and Chelkas Yaakov (Y.D. 217) for similar rulings.