Hi,
this isn't very clear in-game because the purple damage number that pops up above their heads is the a sum of all Spirit Damage that happened in that moment, but these are indeed separate instances of damage. Mystic/Improved Burst only consider the damage done by the ability. Same thing happens with Mystic Shot and Kinetic Carbine, where people wonder why Improved Burst sometimes doesn't trigger when the number is clearly above 125.
Presumably, that's why things like Quicksilver Reload and Mystic Shot explicitly call it a bonus—as in an extra thing added—whereas Surge of Power (which does work to put skills above the threshold for Mystic/Improved Burst) does not.
When you are on the receiving end, you can see it in the damage summary that these are separate instances of damage:
View attachment 15410
So it's not really a bug, it just unfortunately is somewhat opaque due to the game removing clutter by bunching these number together.
(Tangentially related bonus info; It's also worth noting that Mystic Burst and Improved Burst trigger based on the actual damage received by the target, and not the number you read in the skill description. So the threshold is higher if you use it on someone who bought Spirit Resist or a Hero with innate Spirit Resist like McGinnis.)