On a plane with winglets the source of the vortices change from the wing tips to the top of the winglets. Whether that affects wake turbulence from bigger airplanes is probably somewhat different for each airplane.

Since the whole idea behind winglets is to reduce induced drag, possibly the wake turbulence of big airplanes with winglets might be reduced somewhat. But bear in mind that the jet wash from the engines on large aircraft is still there, even if the vortices have been reduced somewhat.

The same rules apply: after a large plane lands, land your plane beyond that large plane's touchdown point; and takeoff above the takeoff point of a big plane. If possible, stay upwind of the runway until clear of the runway area. And if a controller issues you an immediate takeoff clearance after a big plane has either landed landed or taken off, consider refusing that clearance and waiting a couple of minutes until the vortices either dissipate or move downwind of the departure path. Safety first!