In Introduction to Contact Topology by Geiges, there is a result relating Hamiltonian and Reeb flows for hypersurfaces of contact type in a symplectic manifold.
Lemma 1.4.10 $\,$If a codimension 1 submanifold $M \subset T^* B$ is both a hypersurface of contact type (with contact form $\alpha= i_Y \omega$ for some Liouville vector field $Y$) and the level set of a Hamiltonian function $H: T^* B \to \mathbb{R}$, then the Reeb flow of $\alpha$ is a reparametrisation of the Hamiltonian flow.
Q: This is true in any symplectic manifold (and not just the cotangent bundle), right?
Indeed, the proof supplied by Geiges appears to work in the general case. This doesn't yet appear in the errata, and I just want to get confirmation before sending it in.
Since this is a local statement, and every symplectic manifold is locally symplectomorphic to a cotangent bundle, it is true more generally.
But it's not a typo. The statement of the lemma is correct as it stands. The author may simply not have needed to consider the more general case.