We are having cement steps constructed and the fill used is concrete from the old steps, which I understand... but on top of that there are several shovelfuls of loose dirt. Will the integrity of the steps be affected by this? Thanks!

I'm pretty sure that the dirt serves to fill in the air spaces of the old concrete rubble.
How well it's tamped down might be the important part.
Also how solid your ground is under all this in the first place - did they prepare below grade?

Some depends on how much old will be used, and how much new is going to be mixed, and how the ground was prepared.
Take pictures of each step (hah) they do and ask for explanations as they work.