The problem most likely has to do with the raised bead around the edge of most records. That bead gives the record strength, and in the old days, that bead also kept record surfaces from touching each other when records were stacked for automatic play.
When you set the needle down on the top of that bead, it slides downhill and gains momentum that can carry it past the first grooves it encounters. Do what you have been doing already--set the needle down further into the record. With practice, you will still be setting down before the music commences.