I would have imagined that whatever your search term is doesn’t actually get mapped to a new record, or maps only to the primary field on the record. For contacts I believe that would have been the ‘fullname’ field. But perhaps it’s literally the first field on the main form.
Quick Create is actually a little bit different, it’s a separate form that gets used when you create a new record. It’s a single column form panel that pops open on the right of the screen as a modal dialog. As the name suggests, it’s to quickly create records with as few fields as possible but there isn’t any mapping associated with the lookup that it came from, since in quick create is triggered during any creation even from a grid or view.
the only ‘search’ mapping I know of is the Quick Find search view - it lets you select which columns you are performing a search on, lookup search included.
otherwise you can take a look at the classic UI, open up the relationship to you Contact table from your custom table, and on the left side you’ll see a ‘Mapping’ section. That’s normally parent to child record mapping, not ‘search’ mapping but maybe it helps.
