Is 15/32" Plywood okay for Subfloor under tile?
Most tile and mortar manufacturers want 1-1/4" (nominal) even with polymer-modified mortar. While your joists are unlikely to flex, the subfloor might. I'd use 1/2" cement board if height isn't a critical concern. 

Alternatively, block between your joists on 16" or 19.2" centers. Even vertically-oriented 2x4s would do if fastened well.