Deposits of calcium sulfate scale on the surfaces of industrial equipment in distillation facilities, reverse osmosis desalination plants, in oil and gas industries lead to significant clogging of pipes and membranes and to a serious increase in production costs. For the mitigation of scale formation, the wide spectrum of antiscalants is applied. The present work is dedicated to the study of calcium sulfate deposition from supersaturated aqueous solutions in the presence of polyacrylic antiscalant with fluorescent marker (naphthalimide fragment) PAA-F1, which provides traceability of the scale inhibitor and a better understanding of its efficacy. A paradoxical phenomenon is being described here. Antiscalant causes a change in the crystal phase from bassanite to gypsum, significantly reduces the amount of deposit, but does not reveal the presence of its molecules either at the kink, step, or at selected edge sites of deposited crystals. Contrary to the predictions of the theory, it either stays in the aqueous phase, or forms its own separate phase Ca-PAA-F1. It is demonstrated that the antiscalant does not block the surfaces of calcium sulfate nuclei or crystal surfaces, but rather the foreign particles of nanodust with particle sizes around 1 nm, naturally occurring in any aqueous solution. As a result, the number of calcium nucleation sites is reduced, and the rate of scale formation decreases without any apparent antiscalant–scale interaction. On the grounds of the current experiment, the substoichiometric effect of scale inhibition obtained an alternative, quite stoichiometric explanation.