Non-Hermitian systems driven along slow parametric loops undergo nonadiabatic transitions whose outcome depends sensitively on the driving speed, yet no explicit formula has been available for the critical timescale $T_{\mathrm{cr}}$ at which these transitions develop. Using a $2\times 2$ Hamiltonian with circular parameter trajectories, we derive $T_{\mathrm{cr}}=\mathcal{G}ln(1/|\mathrm{\Delta }\left|\right)$ in closed form for nonencircling loops, phase-shifted loops, offset loops, and loops encircling exceptional points, where $\mathcal{G}$ is a geometry-dependent growth factor and $\mathrm{\Delta }$ is the instability seed. This formula sharply separates the regime where the system remains in the averagely dominant eigenstate ($T<T_{\mathrm{cr}}$) from the superadiabatic regime where the instantaneous dominant eigenstate takes over ($T>T_{\mathrm{cr}}$), resolving the apparent tension between the previous literature. We identify two competing seeds: a geometric Stokes multiplier and the finite-precision floor. When the geometric seed vanishes, precision alone governs the transition, yielding $T_{\mathrm{cr}}\propto mln\beta$, linear in the number $m$ of digits in base $\beta$ (bits for $\beta =2$). For loops encircling an exceptional point, the Stokes seed only sets an intermediate plateau; the final transition is again seeded by the precision floor, and $T_{\mathrm{cr}}$ remains linear in $m$. This provides a purely forward-evolution manifestation of precision-induced irreversibility [L. E. F. Foa Torres, G. Pappas, V. Achilleos, and D. Bautista Avilés, Precision-induced irreversibility in non-Hermitian systems, Phys. Rev. A 114, 012207 (2026)], demonstrating that the fundamental limit identified through echo protocols also controls the outcome of slow non-Hermitian dynamics without requiring time reversal. For PT-symmetric energy spectra, $T_{\mathrm{cr}}$ additionally determines the onset of chirality: the dynamics is nonchiral for $T<T_{\mathrm{cr}}$ and chiral for $T>T_{\mathrm{cr}}$.

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• Non-Hermitian systems
• Adiabatic approximation