Sorry if this a bit of a dim question

Ok, my composition is in Eb major, and one of the variations modulates to C minor (the relative minor). Since they have the same key signature, I don't have to insert a new one at the beginning of that variation do I? I can just put the B naturals in where neccessary? And how do I transpose the variation to C minor? (it's currently in Eb major). I thought it would just require going down a minor 3rd, but sibelius sticks naturals in everywhere! I think it was going to C major
Heelp please!

Minor keys do not have their own key signatures, they share them with the relative major and use accidentals. Going down a minor third would take you to C maj / A min so you'd expect three naturals to cancel the flats in the key signature for Eb maj / C min.

Sibelius is probably not understanding what you are trying to do, and thinks that you want C major...

Transposing is from major to major or minor to minor.
You want the same key signature and if you transpose the key signature will change.

You will most likely have to just put in the new notes.