I think we're getting "being possessed by Ulty" confused with "inheriting the sorceress powers." Being possessed by Ultimecia does NOT give anyone sorceress powers. Everyone she possesses already has those powers, which is WHY she possess them. (For example, Ulty had no interest in Rinoa whatsoever until she inherited Edea's powers.) Ulty wanted to possess sorceresses so that she could use their powers to accomplish her goals - since she could not be there in person to do these things herself (she could only send her conciousness back until time compression was achieved), she would obviously want to possess those who were equally as powerful as she was in her own time.
Now, that said, here is the cronology as I understand it:
1. Edea gets her sorceress powers at age 5 from some sorceress other than Adel. Who this person was is unclear. There must have been multiple sorceresses, since Edea and Adel had to have gotten their powers from different people. Nothing ever says that only one sorceress can exist in the world at a time, just that at the end of the game, Rinoa is the only one currently.
2. Adel is defeated in the first sorceress war and confined. Since she is not killed, her powers remain. However, since no one other than Estharians know how the war ended, others suspect Edea inherited Adel's powers. This is not true.
3. When Squall and Co. are kids, Edea meets a dying Ulty from the future. Edea accepts Ulty's powers, adding them to the ones she already possesses.
4. Ulty, using Junction Machine Ellone, sends her consciousness back in time and possesses Edea. Edea, controlled by Ulty, goes public as a sorceress and begins amassing political power in order to set Ulty's plans for time compression in motion.
5. Edea is defeated by Squall and Co. Her powers are somehow transferred to Rinoa. Sensing this, Ulty possesses Rinoa. Edea is no longer a sorceress.
6. Rinoa, possessed by Ulty, releases Adel. Adel junctions Rinoa to herself. When Adel is defeated, her powers transfer to Rinoa.
7. Rinoa is possessed by Ultimecia. Ellone sends the Rinoa/Ultimecia conciosuness into the past to achieve time compression.
8. With time compressed, Ulty releases Rinoa, since Ulty can now exist physically.
9. Rin, Squall and Co. defeat Ulty. Ulty travels to the past and gives her powers to Edea. Time fixes itself.
Rinoa is still a sorceress. They only one in the present.
Hope that clears things up.