If so, there are a number of things you can do with screws, shims, glue and other material.
I do not know about this apparatus you are referring to, but tightening up the treads will solve the problem. Most cases treads will squeak is because they were nailed to the stringers with smooth shanked nails and over time the wood has worked loose around the nail and it actually rides up and down on the nail making the squeak.
Nothing can be done from the top side as all procedures will show and be seen. All work is done from under. You can actually toenail some stainless screws from the stringers into the treads to pull them down tight to the stringers. do not use too long a screw.
You can also get some homemade oak shims and cram them in between the stringers and the treads to take up this slack then toe nail screws to pull them together.
You can also squeeze some liquid nails between the stringers and treads and then toe nail again.
your main purpose is to stop the rocking of the tread on the stringer. You can do this experiment with a second person. Have them walk the stairs slowly and you from underneath watch each tread and mark them with a pen to show which one and where the space is.
Not a difficult job, just takes time and patience.