Both the Classic and Next Gen Center Tank Scavenge have only one thing in common:
The fact that they transfer the fuel from the center tank to the number 1 tank.
Thats it!!!
They are activated differntly. The scavange circuit for the classic is activated manually. When the flight crew gets the low pressure lights in the center system, the switches are placed off and then on. All this logic is sent to a box (EAU) which activates the scavenge circuit for 20 minutes. This normally takes place when the center tank is pretty much empty.
On the B737NG however, everything is automatic. It activates when the No.1 Main tank is about half full something like 4,300 lbs. At this capacity a float switch is activated which opens the scavenge shut off valve. This allows the flow of fuel from ctr to no.1.
Yes there will be a bit of an imbalance since the no.1 main tank is being supplied with fuel from the center while contunuing to burn its current supply. So the no.1 tank should have more fuel.