Yes the animations in your TotalEffects dir are
Let me put it another way.
You have changed fireyflair.texanim, I searched your .particle files and you have used it in
Now the relevant lines in those particle files are as follows
textureAnimationName "C:\Documents and Settings\Paul\Desktop\stuff\ForgeTools1.1\ParticleForge\TextureAnimations\fireyflair.texanim"
textureAnimationName "C:\Documents and Settings\Staraptor\Desktop\ModStuff\SoaSE\Modtools\PF\TextureAnimations\fireyflair.texanim"
Also you don't have fireyflair.texanim in your TextureAnimations TotalEffects mod dirs.
Now let say you load Sins with your mod enabled, when Sins searches for the file fireyflair.texanim it will find it in the two dirs above. Fine, however those dirs are unique to your machine, so if I do the same thing on my machine (that is load Sins with your mod) Sins can't find those dirs and will load fireyflair.texanim from the Sins TextureAnimations dir, i.e an unmodified fireyflair.texanim.
This applies to any texture, mesh or animation that you, or Bailknight or who ever has modified and is in a unique dir to your machine. Sins on another PC won't be able to find the files and will revert to the original files in it's loadup dirs