Was it doing this at moderate or full throttle? With my 3-season tires i get wheel spin on most roads full throttle shifts into second. The gas pedal does push back on my foot telling me this.

Are your summer tires staggered? You can do a circumference check: a dab of paint on each tire and drive a couple rotations and measure. X-drive not happy if much more than 1% difference. People often refer to shuddering feeling when front and back don't match.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)