I am running into the same issue, you would think unchecking the Auto Activate on the Skeletal Mesh would not activate it but the animations still run.
Here are my findings:
If the Skeletal mesh is a component in a BP disabling the tick on the BP does not affect the component.
To disable the Skeletal mesh component you will need to disable Auto Activate and tick on the Skeletal mesh component and then in the BP you can use activate and deactivate to control the on off state. You don’t need to enable/ disable tick eat time, you just use the activate and deactivate.