Your talking about the behavior of the human eye. That is external to the camera, and has nothing to do with ADDITIONAL lag imposed by the device.
Thats a misconception! While external its also influenced by the camera.
The behavior of you eyes changes with the luminous flux - once the EVF puts significantly more photons on your retina the lag caused by your eyes decreases compared to the OVF. For the lag between the world and your brain you need the sum of both viewfinder- and your own lag.
What you experience happens when the camera can't raise the sensitivity to a degree that allows for a proper exposure while retaining high frame rates an thus chooses to expose longer. But you couldn't shoot action under such circumstances anyway, at least w/o relying completely on flash.