I'm having an issue where the emitter particles are offset from the emitter geometry. This seems to be a problem that's happened to someone at least once before way back in 2013 here:
I'm having the same issue. If I use "halo" as the particle, the particles emit properly from the emitter object. If I switch to "object" they are inexplicably offset from the emitter object.
First image is the halo's around the orange highlighted emitter object. Second image is the particles offset in the -Z direction from the orange highlighted emitter object. The only change I made is switching from "Halo" to "Object" in the "Render as" setting. My particle objects are 3-vertex cones. Nothing complicated. None of the other settings have changed.
I'm in Blender 2.81 on Windows.