Automatically change field when another field value is selected
This sounds like a bad case of data de-normalization. You shouldn't have a "Contact" field on your "Job application" content type if it's simply going to duplicate whatever is already in the "Job" content type.

If you're simply wanting to be able to see who the contact is for a given application, use the "Rendered entity" formatter for the job reference field on the application content type. (I'm assuming you're using the Entity Reference module?) In the formatter settings, choose a view mode that only displays the contents of the Contact field on the job node.

This way, if the contact ever changes for the job, it'll live-update across all job applications.