Can this be installed over floor joists or do you need plywood under it?

It depends on joist spacing- Deflection of all subfloor installations must not exceed L/360 for ceramic tile installations and L/720 for dimensional stone installations over wedi product. Plywood subfloor joist spacing must not exceed 16” o.c. with minimum thickness of T&G exterior grade plywood of 19/32 inch. Joist spacing in excess of 16” o.c. and up to 24: o.c. requires a double layer of ¾” Exterior Grade Plywood T&G subfloor sheets, glued and screwed. Plywood sheets must be installed with a 1/8” gap between sheets. (This info can be found on the Technical Data Sheet Download (page 2) on the product page.)