For real scalar field, we know that the Feynman propagator is defined as $$\langle0|\mathcal{T}(\hat{\phi}(x_A)\hat{\phi}(x_B))|0\rangle=\theta(c\tau)\langle0|\hat{\phi}(x_A)\hat{\phi}(x_B)|0\rangle+\theta(-c\tau)\langle 0|\hat{\phi}(x_B)\hat{\phi}(x_A)|0\rangle$$ where $\tau:=t_A-t_B$. It indicates that a particle is created in a past time and will be annihilated at a future time.
However, I have some trouble to interpret the case for the complex scalar field. For the free complex scalar field, there are three kinds of Feynman propagator:
1.$\langle0|\mathcal{T}(\hat\varphi(x_A)\hat\varphi(x_B))|0\rangle$
2.$\langle0|\mathcal{T}(\hat\varphi^\dagger(x_A)\hat\varphi^\dagger(x_B))|0\rangle$
3.$\langle0|\mathcal{T}(\hat\varphi(x_A)\hat\varphi^\dagger(x_B))|0\rangle$
where this time $\hat\varphi(x_A)=\int d^3k\frac{1}{(2\pi^3)\omega/c}(\hat a(\vec{k})e^{-k\cdot x_A}+\hat b^\dagger(\vec{k})e^{+ik\cdot x_A})=\hat\varphi^{(+)}_a+\hat\varphi^{(-)}_{\bar a}$ which reprerents the annihilation of particle and creation of anti-particle operators respectively, and $\hat\varphi^\dagger(x_A)=\hat\varphi^{(-)}_a+\hat\varphi_{\bar a}^{(+)}$ is the composition of creation of particle and annihilation of antiparticle operators respectively.
Then, through my calculation, 1. can be interpreted as the vacuum cannot create an anti-particle and annihilated as a particle. 2. can be interpreted as creating a particle cannot have an annihilation of anti-particle.
However, I have some trouble to interpret the 3rd case. For 3., according to my calculation, the Feynman propagator is the same as the case for the real scalar field. Nevertheless, the $t_A>t_B$ case being described as creating a particle in the past and annihilate in the future, while $t_B>t_A$ case being described as creating an anti-particle in the past and annihilate in the future. Even though, we know that particle and anti-particle exist as a pair, the above interpretation has some problem that one can only choose $t_A>t_B$ or $t_B>t_A$. That means for some time ordering one can see particle being created and annihilated and for other time ordering, one can see anti-particle being created and annihilated. So, what is wrong with my interpretation? Could you point it out?