I was an organist, not a pianist, until I retired -- and as yu probably know organists, for some reason, almost always work from music without memorizing. I don't know why... so I've worked with a lot of page turners!
Keep in mind your objectives: first, get the page turned at the right time, and I agree that my preference was always at the beginning of the measure before the turn, unless the music was very fast in which case maybe a wee bit sooner. Second, stay invisible while you turrn the page! I would suggest that standing quietly, a couple of measures before the turn (depends on how fast the piece is) and reaching over an making the turn is best. Try to make it so the whole thing is one smooth, relatively slow but continuous movement from seated to seated. If in doubt, though, stand and get your hand on the page sooner than you think you need to rather than later! First place, having the turner not there when you think you need him or her is likely to make the player nervous; second place, if you have to hurry the risk of pulling the music off the stand completely increases, and that is something you do not want to do...