At the Youtube video he underturns 1-3, step 3 backing DW and does a 1/8 between 3 and 4. I don't understand why he does it that way, I would do it as written in ISTD technique.
Step 2 I dance like written in the book "to side, backing DW" and this means NOT going along LOD but following the line DC. In some medal classes for making an easier sequence I teach the Rev. Turn starting facing LOD and doing 1/8 more between 1-2. Even in that situation man doesn't dance step 2 along LOD (like many beginners want), but should dance 3/8 to left between 1-2 to get step 2 moving DC. This step moving along LOD would result in big trouble concerning lady's heel turn, especially her following step 3, because man would drift away instead of dancing AROUND the lady's hell turn spot. With beginners making that drifting-away mistake you even often see the lady stepping OUTSIDE at 3, not able to follow the man.