Disabling modifier in viewport does the thing, but I want to animate it, which isn’t possible with the armature disabled (see this clip).
I look to some posts with the same issue:
model looks different in edit mode than in object mode
Looks fine in Edit Mode, distorted in Object Mode
…and tried this one:
Download the file here.
Vertex weights and bone constraints are ruined. Regenerate the character or rig it manually.
By the way, if you are using an addon, always say so.
Yeah - looks like your bone weighting is pretty broken - with some verts assigned to the wrong bones, or, not assigned at all. You might want to delete your weighting and set it up again.