They are allowed, yes! Since the Refugees are being moved during the daytime, they won't be experiencing any effects while moving to Skytower, and the hope is that the effects won't return, since Chubu (where Skytower is located) is in the East!

While they won't experience any effects at night at Skytower for the first few days, you're welcome to have the effects manifest in them just before things fall into chaos, if you want to have the combo of lunar cursed + lewd shadows in Skytower!