Oxidation state of iron can easily change between +2 and +3. As a result, the phase composition of your sample will be strongly dependent on the annealing temperature and atmosphere. If the iron is oxidized enough, you will observe pure spinel (W. Kwestroo, J. Inorg. Nucl. Chem., 9 [1] 65-70 (1959)), but if the temperature is too high or oxygen pressure is too low, the impurities of MgO and FeO will appear (K. T. Jacob and R. Patil, Metall. Mater. Trans. B, 29B [6] 1241-1248 (1998)).
Well, the sample was heated up to 1550 degC in air atmosphere, which means chances of formation of complex spinel is pretty high. What confuses me is the type of spinel formed: Is it (Mg,Fe)Al2O4 type or Mg-iron spinel and Mg-alumina spinel. If the second case is true, then how will they co-exist? Is there any solid solution between them as I obtained one phase in the microstructure.
I attach below the article by Kwestroo. Your results will be probably quite close to Fig. 2 in this article (supposing that your cooling rate is enough fast). Please, pay attention that oxides are written there as AlO1.5 and FeO1.5, so you will have to recalculate the fractions that you use.