I got hung up on your phrase "This is only a couple of generations, which I do not think is enough for evolutionary effects to present themselves." You seem to think that an evolutionary effect involves a change in biology, which I don't think is the case.
Disclaimer: I have not read the full paper, but I do want to make the following point:
A single generation can be well enough for an evolutionary effect to present itself.
By means of a very simple example, assume there are no men. Every woman will be pregnant exactly once (holy spirit!); due to some gene, 1% of all babies are too large to deliver safely; the babies are all girls; they all inherit the gene of having too large babies; half of them die at birth. Consider this an equilibrium state. Now you introduce CS at time x, saving all babies. Only a single generation later, the rate of too large babies will be approximately 2% (in fact, 200/101) -- close to 100% more!
As a kind of explanation, note that an evolutionary effect does not necessarily mean that babies grow differently; it may simply be possible that the selection of babies of different sizes changes over time. In fact, the paper suggests exactly that:
We demonstrated that due to these three properties weak
directional selection favoring large neonates relative to the
maternal pelvic dimensions is sufficient to account for the high
incidence of fetopelvic disproportion in human populations.
Which, in my opinion, says exactly what I started with: there is not necessarily a change in biology; the observed size change can be explained without assuming any change in biology.
Finally, I feel the wording of your question title reflects that misunderstanding: CS are not affecting evolution (your question title); the selection through CS has an "evolutionary effect" (BBC article) in the sense that it is evolution.