When trying to log in to Primo VE using the USNA Midshipmen, Faculty & Staff option, I got an error saying invalid userid and/or password. The Link for Other Users logged me in using SAML as I expected the first link would.
Primo VE authentication profiles were out of the order. It resulted in the reverse of the two login options: USNA Midshipmen, Faculty & Staff switched to Alma authentication whereas Other Users resorted to SAML.
Resetting the profile order resolved the issue: Alma > Configuration Menu > Discovery > Authentication > User Authentication > set SAML as profile 1 and Alma as profile 2.