The rule says something like "pitching restrictions begin when F1 intentionally contacts the plate." What they really mean is something like, "pitching restrictions begin when F1 'gets comfortable' on the mound." Otherwise, when F1 contacts the rubber from the side and then steps with the non-pivot foot to place it in front of the rubber (and happens all the time) it would be a balk.
So, in your play, if the action was all at once, smooth, part of just the whole process of taking the rubber, it's legal. IF there was a pause after taking the rubber and then reaching into the glove, it's a balk