If the vinyl or lino that you put down is tight as you say , then yes you can go over it with a few precautions.
You must clean it well, rough up the surface with a belt sander, clean again and use a special thin set that is fortified stronger than the average latex modified thin set.
And most important, allow an extra day ( 2 is better) of drying time . Thats an extra day more than the 24 hr minimum, before any foot traffic is allowed on the floor. Thin set moisture has no where to go when going over sheet vinyl.Needs extra time or the bond between the thin set and lino will break and you ll have loose tile.
Any questions you can e mail me through my avatar and check my qualifications there. GL
20 years in flooring as a store owner/installer