Validation Rule containing $Profile.Name is not functioning correctly on the Offline platform, but behaves correctly online. Offline Validation Rule configuration is already working properly for other rules.
The Validation Rule includes $Profile.Name.
In order for the $Profile.Name Global Variable to be used for an offline validation rule, users are required to have FLS to the Profile_Name_vod__c field on the user object. This formula field stores the Profile Name for offline use.
End user needs to have FLS Read permission to the Profile_Name_vod__c field on the User object.
CRM Help Documentation: Offline Validation Rules