Remember when you were learning to drive a car,it needed focus on seemingly numerous things,now you can do it without even thinking.As with the grip,there are a number of SUBTLE things required that makes all the difference.Its more than which hand is on first, that is an optional piece but important .The majority of pros get the left hand on correctly first.When you watch Erik in the 5 keys vids,he gets the left hand on correctly first,then the right .
Preshot routine is crucial for a consistent grip. I personally hold the club in the right hand down by the end of the grip, aligning the clubface the way I want, then I put the left on first. From there I will re-grip the right hand. Each person has to find their own method for this. Heck, you could mark your grip so you have a reference if you want. I know some people align the logo on the grip to be a certain way so they can grip the club consistently.