The Seers of the Throne are power-hungy, power-mad even, and will do literally whatever it takes to gain it, no matter the cost. And, judging by the opening fiction (nicely legible this time, at least) they tend to be fairly foul-mouthed about it too. They serve the Exarchs, and are granted great power and reward for their services... but their service is aimed at one thing: keeping humanity in its place, preventing them for attaining their potential. Yet they are human themselves, even if even more self-serving than most. They believe themselves better than the rest, perhaps wishing to right perceived wrongs done them before they Awakened, filled with arrogance and thoroughly enjoying the material largesse they receive from their masters.
The clear intent is that the Seers be used as antagonists, but the material in this book is presented in the same way as the other Order books - so if you do have a group who like the idea of vast material wealth and power with a few distasteful tasks required to get it, it might be an option to let them be the Seers. It's more likely that you will have them as enemies, however, so here are the tools to make them really come to life within your alternate reality.
Chapter 1: A History of Loyalty looks at their history as recorded through their own eyes - given their self-serving tendencies, others may beg to differ at many if not all points. It gives a good overview of both their past and present concerns, however as well as a fair bit of detail about the way that the operate.
Then Chapter 2: Serving the Exarchs gets down to the philosophy, beliefs and dogma that membership in this order entails. Complete obedience to the will of the Exarchs is central, no matter what their request, however costly at a personal level or even to your soul. This chapter also describes how they operate and are organised.
Next, Chapter 4: Heads of the Hydra delves more deeply into organisational matters... they are full of factions and sub-groups, sometimes cooperating and sometimes resulting in friction. There are plenty of examples to provide you with ready-made groups to throw at your mages - or have working away behind the scenes thwarting them covertly, often a more likely way of operating. (The Appendix: Antagonists has more fully-detailed individuals, complete with game statistics, to be used as both combatant and non-combatant NPCs.)
Finally, Chapter 5: Gifts of the Exarchs lays out the magical resources that the Seers can access. The usual collection of magical traditions, spells, artefacts and so on to play with.
This is a neat approach, giving some of the major adversaries your mages will face the same type of structure and resources as their own orders have. It certainly provides plenty of scope for machinations and devious plots, and a wealth of suggestions as to how to use the Seers to best effect in your game. For the sake of your mages' souls, though, encourage them not to enlist with the Seers!