It's all about the heat guys. The changes to the top covers that Walter showed in the pics are good for about 10 degrees. It does indeed make a difference; in many cases the problem goes away. It at least shortens the window where the issue occurs. Hot start issues are characteristically like this:
30 seconds or less, or 5+ minutes, it usually starts right up. The critical time is generally in that 2-3 minute range where the heat has peaked, yet hasn't had time to dissipate. Any additional heat evacuation makes a difference, and often that 10 degrees is enough. But if the temp goes up past 90, then the margin of improvement from the top cover is diminished. The reason the saw will restart immediately, but not 2 minutes later is due to the heat sink effect where the cylinder radiates it's heat into the carb while it's not running or receiving any cooling air flow.
Hitting the primer often flushes the offending fuel out of the carb in favor of what's in the tank, unless it's so bad that the primer wigs out like Andy's is doing. I've been cutting the covers on every saw, orange or red that comes into the shop. Both the 62 and 50 CC families. Everyone says it's better, but with the temps being what they are half the guys say it will still happen sometimes.
So, first thing is to cut the top and see what kind of improvement you notice. I just do it with a utility knife. Have done a couple dozen so far without having to reach for the box of band-aids.