In Field Maps, when you select a layer that has Exclusive Visibility enabled, it doesn't display clear radio buttons like it does in Map Viewer. Instead, it continues to show the Check Boxes and display as if both layers are visible, until you close the layer list and reopen it, at which point the originally visible layer is now turned off and the newly selected layer remains visible.
IDEA: Update the UX to show radio buttons instead of checkboxes in Field Maps the same as Map Viewer.

See this demo'd in this conversation: Re: Why doesn't Exclusive Visibility work in Field... - Esri Community