Doesn't it have to exhibit "correctly matching strings return faster ... on a per-character or other tiny chunk basis" in order to work the match towards correctness?
Yes, and it will indeed try by all means to exhibit that behavior -- unless if it's some contrived regex designed to counter this.
The key word here is "short cirtuit" the match, and any regex engine worth its salt will try to do that as much as possible, tranforming the regex to the faster FSM it can.