The original OP question was concerning a third generation SA/DA 4506. There are differences with respect to the DA only S&W design, including a different (or altered) hammer. The OP's disconnector is operating normally.
When activated, or pushed down by the slide. (out of battery) the disconnector in the SA/DA pistols pushes down on the drawbar, which removes the drawbar's influence on the sear/hammer interface. The hammer of the "in battery" pistol can be brought to the rear by firing, or other intervention, but will stand on the sear until the slide closes and the disconnector allows the drawbar "up", restoring it's contact with the sear. Testing the integrity of the disconnector is done in a confirmed safe pistol by pressing the slide backward slightly out of battery. The trigger should no longer function with the slide out of battery, or "not fully closed" position.
In the DA only scenario, the hammer design is unique, and operates directly through a "camming" interaction with the drawbar. The hammer cams off of its seat on the drawbar as the drawbar is pulled forward by the trigger. There is no "double strike" capability. When the slide cycles after firing, the sear in these guns puts the hammer in the "pick up" position for the drawbar, interrupting it's compete downward fall.
Clear as mud.
Carter