The solution from @danschikore will also work in JMP Live.
When refreshing the data via script in JMP Live, make sure to include the virtual join column properties in the script.
Following the example, in the Movie Rentals data script:
:"Customer ID" << Set Property( "Link Reference", Reference Table("Movie Customers.jmp") );
:"Item Number" << Set Property( "Link Reference", Reference Table("Movie Inventory.jmp") );
In the Movie Customers:
:"Customer ID" << Set Property( "Link ID", 1 );
An in the Movie Inventory:
:"Item Number" << Set Property( "Link ID", 1 );