It sounds like the Sync button on the BEATS page is activated. Please try deactivating it.
The Sync button plays and loops the currently selected beat in Addictive Drums every time you press play in your host software (on top of any midi already on the track). This is for previewing purposes, so you should deactivate it when you have dragged and dropped grooves into the host. If you don't, you could experience phase problems that can make the sound dull and unfocused.
Did that help? If not, please tell me more about the problem. What do you mean by "the nice effect on the double snare hit"?