1996 Mazda Protege radiator cap pressure

Hi, yesterday my radiator was leaking. Upper part of 1st chamber from the top hose had tiny holes. The repair man fixed it & I think it was a good repair. I asked him what caused the leak, my engine never experienced overheating since I got the car & Im sure my gauge is working fine. Also he cleaned-flushed my radiator 6mos ago as maintainance.

He had engine turned off(was running idle for 20mins) then he took off radiator cap. There was pressure. He said all air should be going out to the exhaust instead, engine is also putting air to the cooling system. Its possible the radiator cant cope w/pressure thats why 1 chamber had blown off. He added "if I am correct this will re-occur", he advised me to have my cylinder head checked for worn gasket or valve seals to be sure.

My question: Is he correct? I mean he was no mechanic but he was doing good w/his job. He added most of his clients w/the same issue was resolved by fixing the cylinder head.
2nd question: I dont get wet tail pipe anymore when starting from cold engine(in the morning) for 2months already. Does this mean I have a bad exhaust chamber. How could I know & resolution?

Many thanks, I hope you could help me w/my issues. More power.

Regards,
Robert Smith