Back pivot. Usually hiji shime has uke bent over at the waist, the elbow and arm above their body, and shite either sinks or sinks and front pivots. As they pivot, you pivot. It helps if you relax the arm at the same time. If shite isn't clamped on, when you relax the arm and back pivot, you can even drop to your butt at the end of your pivot and back roll out of the control.
There are nasty versions of the waza where you just drop straight down to the mat and tap like crazy. Look for video of Parker shihan applying the ground version of this.