  Owing to exchange interaction between the exciton and magnetic ion, a quantum
dot embedding a single magnetic ion is a great platform for optical control of
individual spin. In particular, a quantum dot provides strong and sharp optical
transitions, which give experimental access to spin states of an individual
magnetic ion. We show, however, that physics of quantum dot excitons also
complicate spin readout and optical spin manipulation in such a system. This is
due to electron-hole exchange interaction in anisotropic quantum dots, which
affects the polarization of the emission lines. One of the consequences is that
the intensity of spectral lines in a single spectrum are not simply
proportional to the population of various spin states of magnetic ion. In order
to provide a solution of the above problem, we present a method of extracting
both the spin polarisation degree of a neutral exciton and magnetic dopant
inside a semiconductor quantum dot in an external magnetic field. Our approach
is experimentally verified on a system of CdSe/ZnSe quantum dot containing a
single Fe$^{2+}$ ion. Both the resonant and non-resonant excitation regimes are
explored resulting in a record high optical orientation efficiency of dopant
spin in the former case. The proposed solutions can be easily expanded to any
other system of quantum dots containing magnetic dopants.
