Preparing a subfloor is an essential step for installing floor tile it provides a level surface that will allow the tiles to properly stay in place.
Proper subfloor for ceramic tile.
A plywood subfloor must be structurally sound and able to support the installation.
Laying tile on plywood.
Proper preparation of the subfloor is critical to the success of your ceramic tile installation.
It sounds like your joists are well within the acceptable limits of l 300 so your main concern is the deflection of the subfloor between joists.
It will break or dislodge if the surface bends under the load.
Cement backer board can provide a solid flat surface to install tiles on if you have a wood subfloor.
Tile floors are heavy and tile is a hard material.
With ceramic tile you also need to limit the deflection between joists which is a function of the subfloor thickness and how it is installed.
Because of issues of moisture movement and adhesion ceramic tile will work well with certain types of subfloor underlayment systems and can go dramatically wrong with other subfloor materials.
However you re not out of the woods.
For this reason ceramic and porcelain tile floors can be considered somewhat delicate despite the inherent strength of the material.
Wood building materials contract and expand at different rates from natural humidity and exposure.