The phase offset of quantum oscillations is commonly used to experimentally diagnose topologically nontrivial Fermi surfaces. This methodology, however, is inconclusive for spin-orbit-coupled metals where π-phase-shifts can also arise from non-topological origins. Here, we show that the linear dispersion in topological metals leads to a T²-temperature correction to the oscillation frequency that is absent for parabolic dispersions. We confirm this effect experimentally in the Dirac semi-metal Cd₃As₂ and the multiband Dirac metal LaRhIn₅. Both materials match a tuning-parameter-free theoretical prediction, emphasizing their unified origin. For topologically trivial Bi₂O₂Se, no frequency shift associated to linear bands is observed as expected. However, the π-phase shift in Bi₂O₂Se would lead to a false positive in a Landau-fan plot analysis. Our frequency-focused methodology does not require any input from ab-initio calculations, and hence is promising for identifying correlated topological materials.