Every time you open up a cube carb you replace the gaskets & diaphragms
This is why just about every brand does a G & D kit and a rebuild kit.
And no the engine is a one way device unless it is running backwards air can not go from the muffler into the combustion chamber while the unit is running
IF fuel is running out of the muffler then way too much fuel is entering the engine
Only three ways for this to happen
1) the metering diaphragm is split or holed
2) the metering needle is not holding the fuel back ( basically the same as a float valve failing on a mower engine ) .
Number 2 can be from crud in the seat preventing it sealing, a bad needle or way too much pressure in the fuel tank ( failed breather )
3) check valve stuck open on rotary valve carbs ( sorry too lazy to look your carb up )
If you sprayed carburettor throttle & body cleaner through the holes then unless it was a can of the very expensive Walbro carb spray then chances are you have destroyed the needle & every check valve as std carb spray softens the viton rubber used to make a seal so the carb is now trash as the check valves are no longer a replaceable service item .