"The leg division into 1 should not cause your body to lower. Remember that as the moving foot passes the standing one, the standing heel will come up - this lets the standing ankle help maintain body altitude. Between 1 and 2, a similar rising of the ankle is also what begins the swing."
I have to correct my previous post based on new information.
At the completing of step 1, we must start the upswing by raising the heel before the moving foot passes on it's way into step two. This is why the footwork is given as HT - initially heel, but toe by the end of the step which is defined as the time the new moving foot passes.
However, I was wrong about the case between 3 and 1. Here we are actually just finishing the lowering at the end of three, so we do not want to create rise yet. As a result, the standing heel will still be down as the moving foot passes, and will come up only a little before the moving foot pops up into its heel lead. This should have been clear because the footwork is TH - the heel is still in contact when the moving foot passes, wheras my version would have been listed as "THT", which it clearly is not.
This does unfortunately ruin my "easy" advice for how to avoid double lowering. The best I can say is to make sure to lower complete on time, and make sure to really actively use the foot as you prepare the step. While the heel stays down, the weight obviously still moves very far forward in the foot, to support your body until the moving foot is in position to take weight.