The supervising provider setting is used in encounters to both track in records as well as to determine the correct user to use to populate Vaccine Certificates.
To set this value for a given encounter, you can do so via the encounter context menu:
This will open the provider selector:
Once the new provider is selected for this encounter, printing the Vaccine certificate will use this value:
The default supervising provider can be set for an individual user on their profile page via the associated control:
This default will then be used for any encounters opened after this has been set.