To make the level three menu work you must select the column in that table that holds the id from the previous table then select nested for the filtering. This will automatically filter out the third level menu items so that they relate to the id from the level two menu.
The normal relationship of information like this would be:
The table that you use in the level three menu must relate to the table used in the level two menu. You must select the id for the third table that corresponds to the id from the second table. Your tables data must fit the one to many model as it goes down.
Each record in the first table should relate to multiple records in the second table. Each record in the second table should relate to multiple records in the third table. If your data does not look like this then it will be difficult for you to have the menus setup like you have described. Please explain how these tables and records relate to each other with examples if you have any further trouble with this.