Shielding effects and atomic size
Aluminum and gallium are on different periods. When an additional shell is (fictitiously) added to aluminum, the size is seen to decrease. This is, as correctly mentioned, due to the poor shielding offered by the $(n-1)d$ orbitals to the incoming electrons in the ultimate $p$ subshell.

However, between copper and zinc, the matter seems to be different–their electronic configurations are different.

While copper has a $4s^13d^{10}$ arrangement, zinc has a $4s^23d^{10}$. I would presume the fully filled spherical $4s$ orbital to considerably repel (also read as: shield) the d-electrons,  and hence the effect appears as a minute increase in size.

There can be deeper discourses, but I think this should suffice for now.