If anything i would use 3 4 exterior plywood over the styrofoam and then an isolation membrane and tile over that.
Tile over foam insulation.
2x2 foot foam tiles are easy to install over concrete tile or any hard flat surface for basement floors kids room and home exercise areas.
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No neither ceramic tile nor wood flooring should be installed directly over rigid foam insulation.
The other way you could approach it is by using a heating pad over the concrete floor with tile i d also use a isolation membrane here over it.
If your basement slab lacks sub slab foam you ll have to install the insulation above the slab.
It comes in standard size 4 8 sheets and smaller sizes in many different thicknesses from 1 4 inch to 2 inches.
I usually stick them down with ardex x7r or mapei keraquick lay the ufh slc with arditex na or mapei fibreplan then tile with x7r or keraquick subject to the type of tiles being fixed.
It s important that there is no movement under the tile.
Both require an isolation board or slip sheet.
You can use either one or two layers of plywood or osb and the subflooring can either be fastened to the concrete with long tapcon screws or it can simply float above the foam.
Foam board insulation is easy to use and is a great diy way to add some insulation.