You can put rexes outside as long as it isn't going to freeze. Keep in shade for a week before moving to the edges of the shade if you want to get it grow as much as possible in summer. When it starts getting chilly you should start spraying it with fungicide to keep mildew spores at bay - this should help when you move it back indoors for winter. Rexes are one of the begonias notorious for mildew.