Why commutation relations is applied in normal order for antiparticle relation ($t_1<t_2$) in wick theorem

I am reading Wick theorem from "Student Friendly Quantum Field Theory" By Robert D. Kaluber. I understand how normal orderd vanishes and only contraction remains. But in page no. 205, it is stated that when $t2>t1$, then by the definition of normal order, we always put annihilation operators are always on right side of creation operator and in equation (7-84) page 205, It is accordinly as definition and only second term of equation is made normal order using commutation relations.

But in next step when $t1<t2$, it has stated that everything remains same but author have expanded the third term also (unlike previous step where it is already considered as normal order and only second term was expanded ) using commutation relations although it is already in normal order.

Why it was necessary. isn’t this is already in normal order, then why it required to expand using commutation relations? Thanks