The nut on the RS guitar is only a string guide. It keeps the strings equally spaced and in alignment with the tuners.
Each slot is cut deeper than the zero fret in order for the strings to sit on the zero fret. The strings should not touch the bottom of the nut slots.
It is advisable to use some kind of lubrication in the nut slots to prevent the strings from sticking.
There are many products available but a good lubricant is Vaseline.
Just a small amount can be applied (with a tooth pick or similar tool) to the nut slots when fitting new strings.
Clean off any excess with a cloth or tissue paper.