  We report a de Haas-van Alphen (dHvA) effect study on the Dirac type-II
semimetallic candidates \emph{M}Al$_3$ (where, \emph{M} = V, Nb and Ta). The
angular-dependence of their Fermi surface (FS) cross-sectional areas reveals a
remarkably good agreement with first-principle calculations. Therefore, dHvA
supports the existence of tilted Dirac cones with Dirac type-II nodes located
at 100, 230 and 250 meV above the Fermi level $\varepsilon_F$ for VAl$_3$,
NbAl$_3$ and TaAl$_3$ respectively, in agreement with the prediction of broken
Lorentz invariance in these compounds. However, for all three compounds we find
that the cyclotron orbits on their FSs, including an orbit nearly enclosing the
Dirac type-II node, yield trivial Berry phases. We explain this $via$ an
analysis of the Berry phase where the position of this orbit, relative to the
Dirac node, is adjusted within the error implied by the small disagreement
between our calculations and the experiments. We suggest that a very small
amount of doping could displace $\varepsilon_F$ to produce topologically
non-trivial orbits encircling their Dirac node(s).
