The only way I know that you can get pressure back through th carb and possibly the fuel lift tube is because of crank case compression . You say two tubes into the tank... interesting . One may be a return but that's not common on a two stroke as there is often a tiny needle valve in the carb .
Though that said when the diaphragm pushed one way it may also push on the return stroke so could well be a return line to stop the diaphragm rupturing under back pressures if added ethanol fuel is used .
I also wondered if it is a breather tube for the fuel tank, though most fuel tanks have a breather in the filler cap .. they do get blocked sometimes and cause a form of fuel starvation as the fuel in the tank is used a slight vacuum starts to develop in the tank . Which makes them almost impossible to start till the vacuum is broken ( undo the fuel cap and then re tighten it ..if it cures the problem look carefully at the fuel cap for a 0.04 mm breather hole .. they're often found in the wings of the cap , use a strand of copper wire from some electrical flex to " proggle" it clear . Then wash the cap in clean petrol before you put it back on as you don't want the crud going in the fuel tank .
Does your machine make a ( Wait for it ,wait for it
) wow wow wow wow wow ....................sort of up and down noise when it's running on full throttle rather than a deep throaty continuous roar ?
If it is rising and falling it indicates crank case compression ?
If so you have a worn barrel & piston & only a repair will sort it out .
You can check it out by removing the silencer and looking in the port to see the side of the piston , it should be clean slightly oily & shiny not matt or scratched .