I must first define 'presence' in a way that includes only what is relevant about being present at a place. My point is that then 'omnipresence' can happen in way that isn't too hard to understand and even to practice!
PRESENCE: We say that you are present at a place if you can:
1.) Influence the things happening at that place.
2.)Be influenced by the things happening at that place.
If, for instance, a psychic in Andromeda can somehow put off a fire in some forest on earth, which we can't, then for that particular matter, the psychic is nearer to the earth than we are! Being 'near' to a place in the usual way we tend to understand 'nearness' isn't the relevant thing. The fact that you can influence things in the room is all that matter and that is why nature took you 'near' that room.