Why are my Blender model's bones incorrectly rendered on "Animation"?

I’ve been using Blender for like 10 years making 3D content for just about every game engine out there, and actually Blender is probably one of the best to do it with. I laughed my butt off when talking to some of my 3ds Max buddies, as they had no clue you could export an FBX with multiple animations. Literally Max users only got this functionality a year or so ago, when I’ve been doing it for more than 8 years. Earlier this year, I was even able to bring in a groom object for hair and fur, created entirely in Blender. You just have to set up the objects correctly, and export it all correctly. Nothing all that fancy or different from any other engine.