  The band structure of type-I (In,Al)As/AlAs quantum dots with band gap energy
exceeding 1.63 eV is indirect in momentum space, leading to long-lived exciton
states with potential applications in quantum information. Optical access to
these excitons is provided by mixing of the $\Gamma$- and X-conduction band
valleys, from which control of their spin states can be gained. This access is
used here for studying the exciton spin-level structure by resonant spin-flip
Raman scattering, allowing us to accurately measure the anisotropic hole and
isotropic electron $g$ factors. The spin-flip mechanisms for the indirect
exciton and its constituents as well as the underlying optical selection rules
are determined. The spin-flip intensity is a reliable measure of the strength
of $\Gamma$-X-valley mixing, as evidenced by both experiment and theory.
