As a push mower engine is stopping unburned fuel is pumped into the muffler where it very slowly dissapates
When you pull the starter the hot / burning exhaustignites this gas in the muffler which causes a pressure wave pushing the piston down when it is trying to go up.
Second pull has no unburned gas in the muffler so off it goes
You may have a partially blocked exit hole due to mud wasps building there over winter .