By Default, Domain information will not show up for any fields. For ArcCatalog to show domain information within Field Properties, whether it be Text or Long Integer, it will need to have the appropriate field type domain in your database. In other words, if you don’t have Text domain defined, domain information will not show up for Text field in ArcCatalog. Based on the testing, it seems like this is a normal behavior for ArcCatalog. The display of domain information within field properties is triggered from the types of domains that are available within the database. I would like to see domain information show up for all fields with any domains.