Change to command block chain takes two ticks to take effect

Minecraft appears to lag at least one tick behind in its view of a command block chain after the command blocks in it change.

This seems to make it impossible to update a command block chain at a frequency higher than 10 times per second (which is problematic when other stuff runs 20 times per second).

I include the simplest case I found of this happening.

Reproducing:

1. Build the command block contraption in the attached picture.

2. Push the button.

Result:
The 3rd command block from the right appears to disappear immediately.
The following is output in chat during the first two ticks after the button press:

[@] bye
[@] bye

Expected result:
The word "hi" not appearing is understandable since the block stops existing. However, "bye" appears twice despite the fact that there should be nothing connected to that block after the first tick.