At our institution, real corneal abrasions seem to be diagnosed in the PACU, in which case we (the anesthesiologists) would call ophtho. They're typically painful enough that it'd be surprising that a patient could get an abrasion perioperatively and not raise the issue until they get all the way to the floor. We do, however, see chemosis, swelling of the conjunctivae, sclerae, and lids, often as a result of extreme positioning (steep trendelenburg for prostates, prone for spines), which can be irritating but not so painful that they always bring it up right away.
In any case, the anesthesiologist should be made aware, and a diagnosis should be made by an ophthalmologist. Who actually makes the phone call is probably a matter of timing and institutional culture.
We recently had a run of "eye injuries" associated with robotic prostate surgeries (STEEP t-berg), most of which were probably not real abrasions, but rather chemosis. Without the urologists pointing the cases out to us, we wouldn't have uncovered the pattern and identified that 1) these probably weren't true abrasions and 2) some of the risk factors (patterns of fluid replacement, styles of eye taping) that might exacerbate the problem.
