Offline backups is typical for Oracle, not needed for Sybase ASE
Sybase ASE performs database backups in 3 phases, this you can also see in your backupserver logfile. It tries to get as much as possible the latest changes in the backup file.
There might be some open transactions while the backup is made (that is the transaction is not completed when the 3rd phase of the backup finished), these open transactions will be rolled back when the database is put back online. If you would have additional transaction log backups, these should be applied before the database is put back online.
Because open transactions are rolled back when the database is put online, your database will always be in a consistent state.
Note: In latest Sybase versions there's an extra config option 'optimize dump for faster load' to add extra iterations to the backup. This reduces the time needed for the restore, but requires more time for the backup.
Alternative way is to quiesce your database and make external backup of your data files.