It is dangerous, and something is wrong. Find another mechanic. Or take this post back to your mechanic for things to check.
One possibility is a leak in the evaporative emissions control system that recovers gas vapors from the gas tank. This system has several hoses that run from the gas tank into the engine compartment, as well as solenoid valves that open and close. One of the hoses or valves may be leaking. This can be checked by doing a smoke test on the evaporative emissions system and finding where the smoke is coming out.
Another possibility is that the charcoal canister that absorbs the gas vapors is saturated with liquid gas from over-filling the gas tank.
Another possibility is a leaking fuel injector seal.
My guess would be a leak in the evaporative emissions system, since these are hard to trace and can’t be found by looking for a leak of liquid gas, which someone has presumably done. Have a smoke test done.