  We combine low energy muon spin rotation (LE-$\mu$SR) and soft-X-ray
angle-resolved photoemission spectroscopy (SX-ARPES) to study the magnetic and
electronic properties of magnetically doped topological insulators,
(Bi,Sb)$_2$Te$_3$. We find that one achieves a full magnetic volume fraction in
samples of (V/Cr)$_x$(Bi,Sb)$_{2-x}$Te$_3$ at doping levels x $\gtrsim$ 0.16.
The observed magnetic transition is not sharp in temperature indicating a
gradual magnetic ordering. We find that the evolution of magnetic ordering is
consistent with formation of ferromagnetic islands which increase in number
and/or volume with decreasing temperature. Resonant ARPES at the V $L_3$ edge
reveals a nondispersing impurity band close to the Fermi level as well as V
weight integrated into the host band structure. Calculations within the
coherent potential approximation of the V contribution to the spectral function
confirm that this impurity band is caused by V in substitutional sites. The
implications of our results on the observation of the quantum anomalous Hall
effect at mK temperatures are discussed.
