The user account holds the externalAuthId
runtime.properties specifies the URI of the matching property
The profile page must have a property with that URI whose value matches the externalAuthId. (The property value is either a String or an untyped literal.)

A user account may have an externalAuthId

...

I don't know what would happen to a user with more than one one externalAuthID. Probably VIVO will arbitrarily choose among them.

runtime.properties may contain a value for selfEditing.idMatchingProperty

You can confirm this value by looking in the vivo.all.log file in Tomcat logs. Each time VIVO starts up, the first entry written to the log contains all of the properties from runtime.properties. It helps to inspect this if you might possibly be reading the wrong runtime.properties file.

At Cornell, ours looks like this:

No Format
selfEditing.idMatchingProperty = http://vivo.cornell.edu/ns/hr/0.9/hr.owl#netId

To associate a profile page with a user account, the Individual must have a data property whose URI is the one from runtime.properties, and whose value is equal to the externalAuthId of the user account.

For example, the Individual object that forms the basis for my profile page contains a statement like this:

No Format
<http://vivo.cornell.edu/individual/JamesBlake> <http://vivo.cornell.edu/ns/hr/0.9/hr.owl#netId> "jeb228" .

You can confirm this by logging in as an admin, navigating to the profile page, clicking on "edit this individual" and then the button labelled "Raw Statements with this Resource as Subject"
In the example above, the "netId" field is set to an untyped Literal. A String Literal will work also.