Ok, I have one of these and of course, mine runs perfectly quiet. So, my guess is your missing something - but what?
In the exploded view below, the locking ring portion (H) of the motor housing (I) slides up into the plastic filter housing (A) just like in the picture below, then you rotate the motor housing (I) clockwise to lock it into place. Assuming you have that correct, lets move on.
The impeller (G) slides down a stainless steel rod inside the motor housing (I) with no rubber plug on the top end so that should be pretty straight forward.
Sitting inside the plastic filter housing (A) is a removable piece of plastic (F). This is the top part of what what the impeller (G) uses to generate water flow. I believe there is only one way to install this but, for argument sake, the small round hole should go to the back right (look close in the picture below and you will see the small hole and its placement).
Only other thing I can think of is the angle adjustment (J). This is used to get the plastic filter housing (A) to sit level on your particular tank. Can't imagine leveling the plastic filter housing whould make a big difference on noise, but it might (think making the impeller sit perfectly vertical VS leaning a bit).