DR ChasSmith, I've always operated on the theory that the trill is determined by its position in the chord, unless the composer/arranger specifies differently. So, if the key is C-major and the trill is on E, its upper note is F-natural unless determined otherwise; similarly in the same key, a trill on G would be a full step to A, unless indicated otherwise. So, in the example you posted, the trill on A-flat would trill to B-flat since it's in the chord of A-flat minor..
I don't think the world is prepared for my theory book!