Any plant that makes a good ground cover, will spread.  That is often listed as aggressive.  But there are many levels.  Lily of the Valley are almost impossible to get rid of once established as they spread with underground roots and any portion of the the root remaining will produce more plants.  Lamium, on the other hand, will root along the stems that lay on top of the ground.  If they develop somewhere you don't want it to be, you simply pull it out.  The Heucherellas are a clumping plant so they don't spread, only get a bit larger.  They also are a short lived perennial in Minnesota. 
Rather than a ground cover, perhaps you should consider mulching under your trees and plant a few shade loving perennials for color.  There are many.  Visit your locally owned garden center in the spring and check out what is available.+