That is much how the skill is supposed to be taught in the OW class, although there are several ways to hold the mask during the process (step 3). Unfortunately, the way it is taught by most instructors creates an inherent problem in the process. The fact that you said this is not how it is taught in OW training tells me that you were a victim of this problem.2) be level (on a straight line parallel to sea bottom) - dont look back yet.
3) grab mask "manly"/firmly with both hands both upper and lower part of mask.
4) start exhaling strongly through nose before starting to look up, don't exhale through regulator as bubbles might come up to you again.
The problem is that students are usually taught while kneeling on the floor of the pool. putting them in a decidedly different position from the one you describe in step #2--the normal diving position. The problem this creates is that students are usually still taught to do step #4 in your list, even though it is wrong to do it that way in that position. The purpose of looking up is to make the bottom skirt of the mask the lowest point so that the water will run out the bottom when you exhale through the nose. When a diver is kneeling, the lower skirt of the mask is already at the lowest point, so tipping the head back is unnecessary and even counterproductive.
Divers who are taught to clear the mask while kneeling frequently struggle to clear the mask while swimming and have to find a place to kneel. As I wrote earlier in this thread, I am sure that is what happened in the incident that started this thread.