As suggested/// confirmed w/ multiple players while wearing Pyrebrand myself that the unique class set animation does not display to others (only myself). I have heard the same for other class sets such as Warden's 'aerie's cry' set.
Wuuffyy,
WW/berserker playstyle advocate (I play ALL classes proficiently in PvP outside of WW as well)
ESO player since 2014 (Xbox and PC for PTS)
-DM for questions