If I understand the full apparatus to a Simrig, it records the emotive and physical tracks of the person wearing it.
So if that person was a Mage, it might pick up his responses to austral stimulus, but probably wouldn't let some actually 'see' or 'sense' the astral. Basically, the Mage sees something funny, the Simrig records the humor track. The the next person comes along and slots the DL... He feels the humor, but doesn't really understand why (due to the lack of any other input) I base this on the fact that even blind mages can perceive the astral.. Do astral sight is not tied to the visual cortex.
In the case of a vessel taken over by a spirit, it would still only pick up the vessels neural impulses, whatever they are. Probably a blank emotive track if the vessel is not aware (catatonic, deeply sub pressed, etc) or maybe is utter sense of confusion and stark raving panic of his body not responding to his own wishes (DM's call what the possessed vessel 'feels' while being possessed. It would not pick up the spirit's emotions because, 1: the spirit is a formation of mana (and only mana) thus it has no electrical 'wiring' for the rig to mesh to. 2: the emotions of spirits are alien even to the summoning mages (and a host of SR lore/conjecture surround them) it would be like trying to understand the recordings of a Simrig calibrated for a human, but placed on a lemur... At best it would be gibberish, at worse, harmful!
As for the inhabited person, see my response above.