He promised he'd help her out until it got to be too much hassle at which point he'd stop. Absolutely no way he'd go into danger for some rando - he's doing this to protect his reputation, no other reason. When she was captured in the WN, he only really went to save her because they were holding someone else captive that he really wanted to kill, so it was a two-birds-one-stone situation. He may well have left her otherwise.
Now, this is a different situation to that of course, and Akira's slightly different too, but it's more-or-less the same in that Sheryl is someone he probably doesn't even consider a proper friend and her gang are basically irrelevant to him. He helps out because he thinks it's good luck to offset his other actions. His "promise" with Alpha's not comparable - that's an actual contract, he holds those ironclad. His deal with Sheryl isn't one of them.