The excess gas simply goes through the inspiratory limb, past the Y-piece connected to the ETT, and into the expiratory limb. From the expiratory limb, the scavenger removes excess gas, approximately equal to the FGF delivered.
As for how the FGF changes tidal volume, it depends on the liters per minute of FGF, the breaths per minute and the I:E ratio. e.g. if the FGF is 6 liters per minute, that equals 100 mls per second. Lets say the vent is giving 10 breaths per minute and the I:E ratio is 1:2. Every "breath cycle lasts 6 seconds and of that six seconds, 2 seconds is spent in inspiration phase. In 2 seconds, the vent delivers an additional 200 mls (remember 100mls per second FGF). So if you've got 600 mls tidal volume set on the vent, the patient will be getting 800mls.
You're right, the newer vents (narkomed 6000 comes to mind) have a mechanism that keeps the FGF from changing the set tidal volume. It works OK but can still cause problems with low tidal volume settings and high FGF (i.e. at the end of a pediatric case)