I have the coopers kit and mine is doing the exact same thing.
I wouldn't worry though!
The function of the airlock is to allow the CO2 to escape and not allow outside air in. If enough 'sputters' out that you no longer have the 'exit side' globe pretty full I would just boil a little more water and add it to that side.
The bubbles will go through the water just fine. The fact you have the majority on the exit side only tells you you are doing it right. You have positive (outbound) pressure so wort is working and nothing (such as 'bad' air) is getting in.
I am a n00b too but that's MY take on it. YMMV?
