Fermion LSZ reduction / Greens function

In Matthew D.Schwartz book, ‘Quantum Field Theory and the Standard Model’ page 227/8 he talks about Feynman diagrams in QED, specifically $e^{-}e^{-} rightarrow e^{-}e^{-}$ u and t channel tree level scattering amplitudes.

He then proceeds to say that these two diagrams represent contriubtions to the fourier transform of the greens function $langleOmega| T psi(x_1)barpsi(x_3)psi(x_2)barpsi(x_4)|Omegarangle $ where $x_1,x_2,x_3,x_4$ correspond to the two incoming electrons and two outgoing electrons respectively.

My confusion comes from the fact that $psi(x)$ annihilates an electron/ creates a positron. With $t_1<t_3$ and $t_2 <t_4$ then surely the bars are on the wrong spinors; to me this looks like positron- positron scattering.

Edit:
I have found a source that has the LSZ reduction formula for fermions (http://fma.if.usp.br/~burdman/QFT1/lecture_14.pdf). Page 4 it derives the LSZ reduction formula for $e^{-}e^{-} rightarrow e^{-}e^{-}$. Ignoring the pre-factors and post-factors (which, to my understanding, forces the contribution of the greens function not relevant to the scattering problem to be zero?) it shows the relevant correlation function for the problem does indeed have the bars on the opposite spinors (formula 14.10). So this is a mistake in the Schwartz book?