Tagging Contacts from Permanent placements is not easy or straightforward.
There is an Employment type that can be used in a contact search - this is designed to allow you to enter the Employment type of the Contact, so may not be useful in this instance.
The tag options from a placement search relate to the Applicants within the placements and not the client contact.
Please speak with your Account Manager or Customer Success Manager if you would like to review this further.