FePt is the primary material being considered for the development of information storage technologies based on heat-assisted magnetic recording (HAMR). A practical realization of HAMR requires understanding the high-temperature phase transition behavior of FePt, including critical exponents and Curie temperature distributions as the fundamental HAMR media design characteristics. The studies so far found a significant degree of variability in the values of critical exponents of FePt and remain controversial. Here, we show that at the heart of this variability is the phase transition crossover phenomenon induced by two-ion anisotropy of FePt. Through Monte Carlo simulations based on a realistic FePt effective Hamiltonian, we demonstrate that in order to identify the critical exponents accurately, it is necessary to base the analysis on field-dependent magnetization data. We have developed a two-variable finite-size scaling method that accounts for the field effect. Through the use of this method, we show unambiguously that true critical exponents of FePt are fully consistent with the three-dimensional Heisenberg universality class.