I know that at one time SAFC directly employed people. Chaperones, chauffeurs, and even the stewards. However that seems to have changed now and alpha security certainly appear to employ stewards, outside stewards re roads (I actually wonder what powers they actually have in performing these roles). As I have mentioned before, the steward who tends to behave inappropriately (trying to be diplomatic here) is definitely employed by Alpha security and not by the club.
I suspect the club has given tasks on a contractual basis to Alpha and that contract will run until it ends. As it is an employee employed by a n other, I do doubt that the club has any right to discipline. That would be up to his employer.
I would suggest, that it would be important to bring to the attention of the stadium security manager any inappropriate behaviour by stadium / stewarding staff.
I think it is clear what is inappropriate behaviour.
So if people have complaints, put them in writing, in a polite manner being factual and concise and send the to the security manager at black cats house.
The security manager will need evidence of inappropriate behaviour and by whom in order to further influence this action.