I assume that your post relates to the Topic (i.e the tree).
That being the case, if the tree is above the stratum of the Lot (as shown on the Strata Plan) then its removal is the responsibility of the Owners Corporation; exclusive use or not.
Conversely, if it’s entirely lower than the stratum of the Lot, then it’s the responsibility of the Lot Owner.
There’s no need for an adjudicator unless there’s some disagreement about that responsibility.