Comparing different approaches to HMS for elliptic curves

Question

I am trying to understand homological mirror symmetry for elliptic curves from the article of Zaslow-Polishchuk and from Section 6 of the article of Abouzaid and Smith on homological mirror symmetry for $T^4$. Neither discusses Spin structures to orient the moduli spaces of holomorphic polygons, but in Polishchuk-Zaslow all triangles are counted with the same sign, while Abouzaid and Smith prove a generation result from Seidel's exact sequence for a Dehn twist, whose proof relies on the triangles between $L_0$, $L_1$ and $\tau_{L_0}L_1$ cancelling in pairs. See also the remark at the beginning of Section 17j in Seidel's book for the need of a specific Spin structure to prove Seidel's exact sequence in dimension 2. Then it looks like Polishchuk-Zaslow and Abouzaid-Smith work with different choices of Spin structures, and that would not be a big deal, if at some point Abouzaid and Smith didn't use Polishchuk and Zaslow's computation of the computation of the homological category of the Fukaya category of the torus. Do Polishchuk-Zaslow really use different Spin structures or am I misunderstanding Seidel's exact sequence? If they do use different Spin structures, how is transferring computations from one setting to the other justified?