Is it OK to screw cement backer board over 12 x12 vinyli tile before applying ceramic tile?

Yes , should be fine.

I did it with no problems occurring.

If you do it the way James Hardie spells out in his Hardibacker installation instructions you should screw and glue with modified thinset. Hardi makes special screws for their backer board, I'd use them. I don't think Harold or Smearcase are wrong in their approach but Hardi is safer in the very long run.

I agree with Bob, (mutual admiration society here), those cement screws have a little burr underneath the head that makes sinking below the surface easy.