They definitely do downdraft though it seems the thermal visualisation only shows rising air movement. I flew a glider between two nearby strong thermals with a fairly stiff breeze blowing and I got caught in a major downdraft in between.
Not sure how realistic but its pretty cool, turbulence seems more controlled as well and only occurs as you fly though the thermal variations. I noticed my wing lifting on one side generally as I flew along the boundary of a thermal.