Fly-buck converters provide a compact isolated auxiliary rail, but their transient response is shaped by magnetic coupling, leakage inductance, capacitor equivalent series resistance (ESR), winding direct-current resistance (DCR) and switching frequency. This paper develops an analytical and switching-level framework for conventional and tapped-inductor fly-buck converter (TI-FBC) structures and derives the primary-referred small-signal model of the tapped stage by state-space averaging. The model reproduces the computed pole locations and yields a closed-form zero set by the tap ratio, derived rather than assumed. The zero lies in the left half-plane for the arrangement examined here and in the right half-plane for its complement. The tap raises the damping ratio of the pole pair by an amount equivalent to scaling the inductance, so the zero, not the damping, distinguishes it, and the two mechanisms give the predicted overshoot a computable interior optimum. At a duty ratio of 0.25 the optimum tap ratio is 0.233 and lowers the predicted overshoot from 66.97% to 42.71%. The reduction is specific to the line transient: the tapped structure deviates more under a load release. Three costs follow: the predicted efficiency falls by 2.3 to 13.1 points at nominal loss coefficients, set by the tapped-winding realization; the low duty ratio leaves little modulation headroom; and the peak switch current rises fourfold. A closed-loop study shows that the left-half-plane zero permits a 2 kHz crossover where the complementary arrangement reaches only 1320 Hz. Oscilloscope records from an isolated multi-output module are consistent with the predicted ripple asymmetry.