It would help if we knew what you were driving.
If the vehicle made this noise before, then I'd say it's normal, but if that were the case you wouldn't be asking this question.
I've never heard of "heavy duty" brake drums, nor of new brakes being "grabby." New brakes should operate perfectly, just as they did when the vehicle was new.
I don't know what's making the noise but I think you should take it back and ask the mechanic who installed the brakes what is making the noise.