I am just missing something.
Very simple or so I thought - using jquery - Based on the value selected in the Workers dropdown, I want to display on
Using AJAX is a great way to do what you are asking.
Please forgive me if you already know this but in jQuery/javascript, you:
grab the value of the first select box
use AJAX code to send that to a secondary PHP file, which uses the data it receives to write some HTML code based on what the user chose
the newly constructed HTML is ECHOed back to the ajax routine, where it is received inside a success function
Inside the success function, you can use jQuery to replace the contents of the second dropdown
Here is a detailed example, with explanations