I realised that I'm not understanding a passage in Seidel's [Symplectic Floer Homology of a Dehn twist][1]. more specifically, I don't get why his choice of almost complex structure on $\Sigma$ is a valid one. 

By definition of Floer Homology of a symplectomorphism $\phi$, we need to equip $\Sigma$ with a family of almost complex structures $J_t$ such that $J_{t+1}=\phi^*J_t$.

> at page 832 the author claims that on the neighbourhood of the Lagrangian sphere $[-R,R]\times S^1$ there are standard almost complex structures $\{J_t^R\}$ that can be extended to the entire $\Sigma$ 

The problem that I have is that I don't see why $(T_0^R)^*J_t^R=J_{t+1}^R$. For me the standard almost complex structure on $[-R,R]\times S^1$ is the (constant family) that in the canonical coordinates looks like $$\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$$
but in this case it's immediate to verify by hand that $$(T_0^R)^*J_t^R \neq J_{t+1}^R$$
it's very likely that I'm missing something, but I really don't know what, hence I decided to ask the question once and for all.
> what are these standard almost complex structures on the cylinder that are suitable for setting up the Floer equations in this case? 


  [1]: https://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/1996/0003/0006/MRL-1996-0003-0006-a010.pdf