Should anchors be used with screws going into framing?
If the screws are ONLY in to drywall, take it down immediately and reinstall the screws with the anchors. Drywall will not hold a screw all by itself. With an anchor, the anchor expands BEHIND the drywall, preventing pull-out.

If the screws are very long AND you got them in to the studs, you could be good. But it depends on the type of screws, the weight of the cabinet, and how deep in to the stud you got the screw. Too small a screw and it could pull out or shear off.

If the instructions don't talk about using the included screws to mount the cabinet to studs through drywall, then I wouldn't trust them. Go down to your local hardware store and get yourself some cabinetry screws. You probably want them to be at least 2 inches long so you get a good amount of thread in to the studs.