Previously, high-temperature ferromagnetism with a Curie temperature in excess of 400 K was reported in the magnetic semiconductor (In,Mn)Sb films grown by metal-organic vapor phase epitaxy (MOVPE). To determine the role of Mn distribution on its magnetic properties, the Mn 2p core-level X-ray photoelectron spectroscopy (XPS) of (In,Mn)Sb films was measured. For films grown on an InSb substrate, Mn composition is spatially inhomogeneous and its concentration increases with increasing deposition temperature. Spin-orbit splitting energy of the Mn 2p core-level was found to increase with increasing Mn concentration. From the dependence of the measured spin-orbit splitting energy on the Mn concentration, evidence of atomic-scale Mn cluster formation was observed. The measured magnetic moment per Mn atom decreases from 3.0 μB/Mn to 1.8 μB/Mn with increasing Mn concentration, which is attributed to atomic-scale clusters that are ferromagnetic or ferrimagnetic. This detailed investigation gives an insight into the Mn distribution, phase composition and origin of magnetism in MOVPE-grown (In,Mn)Sb magnetic thin films.