Yes, but you don’t have to do both to maximize your drops.
If you kill Azshara on Normal, you should get some of the drops (x).
If you then kill Azshara on Heroic in the same lockout, you should get some more of the drops (y).
If you skip Normal and go straight to Heroic, you should get the total number of drops (x+y).
Killing Azshara on Heroic, then killing Azshara on Normal will result in no drops of those items on the second kill.
Having said that, we had a data error calculating Aqueous Reliquaries this week, and when we fix it, more will drop. To avoid impacting players who have already killed the bosses, we’re fixing it at the beginning of next week. Starting with next week’s raid reset, the amounts will be corrected.