Popular internal shock models, developed to explain production of high energy flares in blazar jets, involve collisions between local overdensities of matter being ejected by a central engine and moving along the jet with different velocities. Prior to such collisions, the matter is relatively cold and therefore does not produce intrinsic non-thermal radiation. However, due to Comptonization of external radiation by cold electrons, the presence of such matter should be apparent by prominent precursor soft X-ray flares, visible prior to non-thermal $γ$-ray flares. In this paper we discuss the predicted properties of such precursors and study the dependence of their properties (luminosities and light curves) on kinematic parameters of relativistic ejecta and on an angle of view. We demonstrate that the lack of evidence for luminous soft X-ray precursors can be reconciled with our predictions for their properties if acceleration and collimation of a jet takes about three distance decades. We briefly discuss the severe constraints on the internal shock models that would be imposed by a non-detection of such precursors. Comment: 20 pages, 5 figures, accepted for publication in ApJ