Just tested it and Master-at-Arms increases the damage of :
- Puncturing Sweep
- Radial Sweep (Initial Damage & DoT)
- Sun Fire (Initial Damage & DoT)
- Eye of the Storm
- Wall of Elements
- Elemental Touch (Initial Damage & DoT)
- Meteor (Initial Damage & DoT)
- Mystic Orb
- and more I couldn't test because I don't have enough time
(Un)Surprisingly, it doesn't increase Radiant Oppression's damage.
Currently writing a ticket.
When you're attacking an enemy with an ability, if the damage numbers are white or yellow its direct damage. If the damage numbers are orange, its damage over time and benefits from thaumaturge instead.