When you assign LIOs or SLIOs to a source, the control of that logic is determined by the first destination to lock the source.

A destination locks when a console fader turns on or when you right-click a destination in Navigator and select Lock Source. It unlocks when you turn the fader off or when you right-click a destination in Navigator and select Unlock Source.
If a source is used by more than one console, the first console to turn it on gets control. The second console can turn the fader on and listen, but it will not be able to take control of logic until the first console turns the fader off and unlocks it.
If you are unsure of which destination has control, you can see this in Navigator.
Go to the source and click to highlight it in the crosspoint grid and then look in the details pane.
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Go to the source tab of the blade and click to highlight the source grid and look in the details pane.
Look for Destination which has LIO Control.
You will also notice that destinations where the source is routed but another destination is controlling logic will have an asterisk in the Navigator crosspoint grid.