Hi Brennan and Millie
Stairs need to be secure without any movement otherwise you'll eventually have cracked grout or loos tiles. If they move when you step on them .... that's your indication they need to be firmed up from behind.
Now, cement board does not add structural soundness to floors or especially stairs but that doesn't mean you can't use it ... it just means that the existing surfaces need to be sound.
If you can build out the risers so that they are close to the front edge of the nosing it will not only make your job easier but help strengthen the steps. You can do this by sawing strips off a 3/4" exterior grade plywood and screwing them into the risers.
The way I do stairs is one way only, and that is installing a slip sheet, lath wrapped around (overlap ends 2") and stapled or fastened with roofing nails and then a mortar bed 1" to 1-1/4" thick. This takes extra work but it's the best way to build a solid surface for your tiles.
When buying floor tiles try to find a product that also supplies ones with beveled edges for the top of the nosing.
Hope this doesn't scare you away from the job. Maybe some of the other guys here will help with advise to make it a bit easier for you.
