Why does the admin need to "log out"?
If each user is logging in under their own password, the privilege set for their account--not the admin account should control their access privileges.
What sort of "cold start" are you describing here?
Cold start is a file that is Auto Run when the Host computer auto starts each morning. It opens the Main database and each associate file using the Admin security. The file ends leaving the Host up and running. This has worked and is per FMP suggested method.
I recently changed the access privileges in File named "Contacts" to limit Clients to only their created records.
It seems that the Contacts file remembers it was opened by the Admin, even tho the client logged in with their password.
I would guess that you are using FileMaker Pro to host the file over a network instead of fileMaker server.
Better check permissions on that file. Assuming that your client is using open remote to access the file like they should, the password used to open the host has no effect on what a client has for access privileges. Those are determined by the account/password used by the client to open the file.
Is there an auto-entered password in file options on this file?