Pa 30 -- the likely remnant of the Galactic type Iax supernova of 1181 AD -- displays an unusual, firework-like morphology, consisting of radial filaments extending from a common center, where a white dwarf (WD) currently drives a very fast wind (speed $\gtrsim 10^{4}$ km s$^{-1}$). We propose the filaments arose from the Rayleigh-Taylor-unstable nature of the interface between the circumstellar medium (CSM) and the shocked wind launched by the natal WD; the filaments then elongated intact due to the Kelvin-Helmholtz-stable nature of the large initial density contrast between the wind and CSM, supplemented by the slowly declining wind density profile (relative to homologously expanding ejecta). To support this interpretation, we present two-dimensional hydrodynamical simulations and derive the filament properties, including their speed, density, and temperature, all of which are consistent with observations. We suggest the filaments elongate until the wind and CSM densities become comparable at the contact discontinuity, which occurs within 1--10 years, and then truncate because the RTI halts. The subsequent KHI growth timescale across the current width of the filaments is longer than the age of Pa 30, so they remain intact. The filament-less central region in Pa 30 is therefore more likely a consequence of the finite timescale over which the RTI operates, rather than a wind termination shock. In general, firework-like filaments may form in other systems, provided there is a sufficiently large density contrast between the ejecta and its surroundings.