I  don't have any reference, but I think that the idea is as follows:
There is a tubular neighborhood theorem according to which a neighborhood of $M^{2n-2}$ is isomorphic to symplectic disc bundle over $M^{2n-2}$.
Take an almost complex structure J compatible with the symplectic form in each fiber. This gives you a metric $\omega(\cdot, J\cdot)$ on each fiber with associated norm $\|\cdot\|$.

Now take the Hamiltonian function $H(x,y)=\pi\|y\|^2$, where $x$ is the variable in $M^{2N-2}$ and $y$ is the fiber variable. It generates a rotation flow in each fiber, and at time 1, it is back to identity.