I have been adjusting to red dots for the past few months. Hadn't used one prior, other than on a few carbines, which is really different in my opinion.
For me, it has taken quite a bit of dry fire practice to get my muscle memory to find the dot at index. I am also using a larger window than the K models (RTS2), just a tad smaller than the SRO.
I haven't used a cowitness setup, but i think that would be something where you'd want to train yourself to ignore the irons when the dot is on. For me, the idea was i'd have a few less steps with the dot. Rather than lining the sights up with eachother, making sure the space on both sides of the front sight are even, then lining the top of the front sight up with your target, all you do is put the window around the target and move the dot to the point you want to hit.
The biggest trick i needed to learn was to get my hand and arm position to snap right in line so that i could see the dot in (roughly) the middle of the window when i draw. Once you get that down, it feels pretty natural.