As someone who is looking forward to Red Mage and enjoys the lore of the game, I thought I might do a bit of creative speculation.
Lore: Experienced in both spells and blade. The Auburn Watch are both their own research division in Sharlayan lands as well as the guardians of Sharlayan research. Their primary duties are two fold: Protect all Sharlayan property, assets, and anything that may lead to additional knowledge, and observe Sharlayan research groups to ensure protection of Sharlayan assets, and projects.
The most distinguishing feature of a Watchman is their crimson hat which prominently marks them as an agent of the Sharlayan government. It is both a blessing and a curse to be under the watchful gaze of a Watchman. Sharlayan research colonies of particular note are assigned a varying amount of Watchmen depending on their importance. While the Watchmen do not interfere with Sharlayan day-to-day life or research, they follow their duties to an almost fanatical level. Any threats to the Sharlayan nation are solved swiftly by the Watchmen, this includes any limiting the breach of knowledge that is rightfully claimed by the Sharlayan government. On more than one occasion, have they silenced the researcher with loose lips.
Becoming a Watchman means swearing complete loyalty to the Sharlayan nation. The very first watchman swore this oath to his master, a prominent leader and keeper of Sharlayan repositories of knowledge who saw the increasing of security from internal and external threats as a necessity. With his oath came almost unlimited access to secrets from across the ages, this included ancient tomes of white and black magic. Being a notable mind of Sharlayan himself, the first grew fascinated with bettering himself through study, through this he developed his own style of magic. This style is now known as red magic.
Through the years, and as Sharlayan research expanded well beyond its borders. The First Watchmen trained others, holding them to the same oath, and as these agents became more and more prominent. The Sharlayan government officially named the ones who adorned themselves in red, wielding both blade and spell, safeguarding their nation with their never faltering gazes, the Auburn Watchmen.