If one has added depth to a font by increasing the extrude value, how does one change the colour of the extruded faces to be different than the front face?
Titler Pro does not have that feature. Extrusion is always the color of the face.
Remember that an object in TP can have any number of layers that make up the visual of the object. What you should do is have two faces in the object style. One without extrusion and one with extrusion. The one without extrusion should be just barely above the other (layer depth control). The one without extrusion should be the top layer in the style. For example the top layer could be at a depth of 0 and the extrusion below could be at a depth of -1 or -0.5. Something just below the top layer.
You can "fake" it. Get the title the way you want it with the extrusion the color you want. Duplicate that paragraph and make sure you set the position on the "Global" tab exactly the same on the new duplicate. Now turn off the extrusion and change the color of the text on the new duplicated copy. You'll now get a face of the new color you just picked and it will look like an extrusion of the original color on the original paragraph.