Asymptotic giant branch (AGB) stars are considered to be among the most significant contributors to the fluorine budget in our Galaxy. While observations and theory agree at close-to-solar metallicity, stellar models at lower metallicities overestimate the fluorine production with respect to that of heavy elements. We present ¹⁹F nucleosynthesis results for a set of AGB models with different masses and metallicities in which magnetic buoyancy acts as the driving process for the formation of the ¹³C neutron source (the so-called ¹³C pocket). We find that ¹⁹F is mainly produced as a result of nucleosynthesis involving secondary ¹⁴N during convective thermal pulses, with a negligible contribution from the ¹⁴N present in the ¹³C pocket region. A large ¹⁹F production is thus prevented, resulting in lower fluorine surface abundances. As a consequence, AGB stellar models with mixing induced by magnetic buoyancy at the base of the convective envelope agree well with available fluorine spectroscopic measurements at low and close-to-solar metallicity.