I'm reading Lee-Parker, “A structure theorem for the Gromov-Witten invariants of Kähler surfaces”, which studies Gromov-Witten invariants within symplectic geometry. Lee-Parker write (§9, p. 23) that
In Gromov-Witten theory, the GW invariant associated with a zero-dimensional space of stable maps is the signed count of the maps in that space with the sign of each map $f$ specified by the mod 2 spectral flow of the linearization $D_f$ (provided each $D_f$ is an isomorphism).
I would like to understand why this is, but they don't provide a reference, and I wasn't able to find anything discussing this relationship by searching online. I would guess the mod 2 spectral flow appears somehow in the construction of the virtual fundamental class, but I don't know enough about that construction to fill in the details.
Is there a reference that explains why this fact is true?