I /think/ this is related to the EDID support or configuration.

What I do know is that you need specific EDID support when using a DisplayPort KVM because that switches the computer away on a regular basis. If you have multiple screens and a single screen KVM (fairly common) it will do the re-arrangement that you've experienced. With EDID support it keeps both output alive resulting in no re-arrangement.

EDIT: It seems the correct term may be "EDID emulation".