Search over map and ajax search works with custom taxonomies ONLY if you add 1 category to each property. Same applies for action taxonomy. DON’T ATTACH A PROPERTY TO multiple categories or multiple actions.
You can use child categories and assign the property just to child. Then the property will show in results when searching by parent category as well.
How to create a parent/child category.
One of the most important aspect about taxonomies is the way they are added. Always LET WORDPRESS CREATE THE SLUG (title and slugs must always match for search results to be accurate).
Create or edit the category and select the parent category.
Child categories can be on 2 levels:
Attach a property to child category ONLY
When you search for PARENT category all properties from that category + child categories will show on the map and in search results.
How to show all categories (including those with 0 properties) is managed from this setting (it used to apply just for Cities and Areas, but was extended to all taxonomies)