OK, well that’s an interesting symptom. Motor starts and runs OK with the vent closed on the fuel tank??
This engine has a great fuel pump! The plastic tank is collapsing so that would seem to rule out most air leak situations.
Does the engine run OK once it is started? I’m assuming this engine has a carb, again, I’m not a merc guy.
Perhaps the carb is flooding over slightly when you shut the engine down causing it to be to restart hot.. You could try pulling the fuel line and letting the engine run out of fuel when hot instead of shutting it off with the key. Let the engine sit a bit like you normally do, then reconnect and pump up the fuel line. Carb flooding should be considered if the engine starts OK now.
PS- I guess I never answered your question about some sort of one way valve in your fuel tank. Some tanks/fuel systems have some sort of valve set up, some don’t, kinda hard to say.