Well, at least you did some thinking and proposed a couple of personal thoughts instead of just asking for the answer to a homework question. Both observations you make are pertinent.
Remember, a celestial sphere doesn't actually exist. It is an imaginary concept, a simplification based upon our perspective of the universe.
A planetarium, whether it is an old-fashioned one that depicts an earth-bound perspective of the universe, or a modern digital projection system that can "fly" you through space to view the universe from a different place, is projecting a perspective of the view of the universe from a particular place, that is, you see the "celestial sphere" as it would appear from that place. In the case of a view from elsewhere in space, it would be a different celestial sphere from our celestial sphere.
So yes, you would be at "the centre" of the celestial sphere. Maybe not the "very" centre in the case of old fashioned projectors with fixed star fields, as they wouldn't account for the 150 million kilometre imprecision caused by the movement of the earth around the sun. But, as this is an insignificant distance in astronomical terms, that doesn't matter a great deal, so "the centre" is probably a sufficient description.