Question regarding the application of Time Reversal Operator in Expectation Value of Operator in QFT

I just want to make sure I understand what I am doing. Let me write down how I think things should work, and please spot any mistake in my thought process once I make any.

Say I have some state
$$
langle psi_1 | hat{A} | psi_2 rangle
$$
and I want to insert $mathcal{T}^{-1} mathcal{T}$ in the matrix element, where $mathcal{T}$ is the antiunitary time-reversal operator. Then I have

$$
langle psi_1 | hat{A} | psi_2 rangle =
langle psi_1| mathcal{T}^{-1}mathcal{T}hat{A}mathcal{T}^{-1}mathcal{T} |psi_2rangle= (langle psi_1 | hat{A} | psi_2 rangle)^*
$$
where $^*$ denotes complex conjugation. Now let me modify the above equations such that
$| psi_2 rangle = | psi_2(p) rangle$ where $p^{mu} = (E, vec{p})$,
$| psi_1 rangle = | psi_2(p’) rangle$ where $p^{mu} = (E’, vec{p}’)$, and
$hat{A} = hat{A}(z)$ where $z^{mu} = (t, 0, 0, z)$

I expect time reversal to act on each kinematic variable (or space-time) in the following way
$$
(E, vec{p}) rightarrow (E, -vec{p});quad
(E’, vec{p}’) rightarrow (E’, -vec{p}’);quad (t, 0, 0, z) rightarrow (-t, 0, 0, z)
$$
Denoting this transformation of variables with the subscript $_t$, we can write the expectation value of $hat{A}$ as
$$
langle psi_1(p’) | hat{A}(z) | psi_2(p) rangle =
(langle psi_1(p_t’) | hat{A}(z_t) | psi_2(p_t) rangle)^*
$$
This remains true even when
$hat{A}(z) = bar{psi}(-z/2)gamma^{mu}psi(z/2)$.

Did I make any mistake anywhere?