When I login into Daylite on the server machine, it does not create an Offline database.
When you login into Daylite on any client machine, an Offline database will automatically be created upon login except if you login with Daylite on the server machine.
The reason an Offline database is not created on the server machine is because it's data redundant. As Daylite Server Admin already stores the data on that computer, there is no requirement to duplicate the database on the same machine by creating an Offline.
Take the following into consideration: Suppose your database running in Daylite Server Admin is 10GB, if you were to create an Offline database on the server machine, then you'd be copying another 10GB on the same computer, which is not an efficient use of hard drive space.