The rumble happens because the engine's RPMs are falling too low and the engine starts to stall but catches itself and goes back to normal. Watch the tach when you sit at a light next time and you'll see. Mine does it sometimes but it doesn't really bother me. I had a '94 Accord that it used to happen to so bad it would stall out on occasion. My only guess is the throttle cable is a little loose and it's not holding the cable as tight as it used to.

Mind you both are manuals so I could hold the accelerator if it got too bad to get the RPMs up.