Hi,
I believe the best way to get around this issue is to programmatically trigger the search whenever it gets visible when the corresponding menu element is clicked.
There is a code within the plugin to only initialize whenever the plugin gets “visible”, but that is very difficult to check properly – a javascript intersection observer is used, and those can mostly detect if an element is within the viewport, but the parent element visibilities are only considered invisible when an element is either not in the viewport or has a display:none property.
Instead of relying on the proper intersection, I would recommend disabling the auto populate feature overall and instead of that using the javascript API to trigger an empty search whenever the corresponding menu element is clicked.