You didn't select "Create Symmetry Constraints". I'm not sure if it will solve the issue completely, but it will probably make some difference.

One thing I see that may come back to bite you later: You can create sketches that make multiple bodies when padded, but I'm not sure why you would want to with the example in this video. If the sketch is two identical bodies mirrored across an X/Y/Z plane use the part design mirror feature and offset the sketch's attachment not the geometry in the sketch. It works better for that and keeps your sketches simpler, and you get to use symmetry for one side of the two things you are making because the origin will be in the center of one of the objects.
Sketches where the origin of the sketch isn't the approximate center of a single closed wire are annoying later if you want to reference them in other features or sketches.
Are you making sunglasses? ๐
When I do what you did but select "Create Symmetry Constraints" I get a fully constrained result as soon as the Sketcher Symmetry tool is finished. No other action is required.