Heavy ingredients, particularly dough, will cause your stand mixer to move from side to side and certain kitchen surfaces will allow the mixer to walk slightly across the kitchen counter as a result.
This is normal for heavy ingredients. Large professional dough mixers often have large steel stabilising stands surrounding the bowl, a bit like cement mixers, but obviously this is not possible with a domestic machine!
Your stand mixer will be fine but it should never be left unattended during the mixing process. This will not be as noticeable with the heavier machines but care should still be taken.