Ok... here is what I have figured out:
Once you clear the first ward you are supposed to get a phone call and they give you the chance to secure the cell block by hiring more guards and using deployment to place them in the ward you cleared. Make sure you hire the max number of guards you can and then deploy at least 8 guards for this section of the prison and make sure you spread them out to cover each section of the ward. This should trigger the next objective which is to build an infirmary and a morgue and hire 5 doctors.
Once the infirmary/morgue objectives are completed it should trigger the next part which involves the security room. If all of your riot guards are dead then you can select some of the regular guards and have them enter the Security room (this is the reason you should hire as many guards as you can when given the chance during the first deployment). Once you get a guard in there you will go through the story sequence and after its over you should have the ability to freely dismiss and recall your riot guards. Push down on the D-pad to access the Riot guards, choose the squad of guards to dismiss and hit square. Once you have done this you can recall them by hitting up on the D-pad and hitting x for each squad you need to recall.
From there you should be able to go into the next ward of the prison and quell the rioters there. Once all the sections of this ward are cleared (except for the hostage crisis area) you should be given the chance to hire and deploy more guards to keep control of this ward of the prison.
You should now be able to send your riot guards to the last ward (section on fire) and clear the northern section of the building that isn't on fire and that should trigger the last part of the hostage story. After that part of the story concludes you should be able to get firemen and stop the fire, build an armory and staffroom and continue whatever is left to do to finish this story mission.
If the game isn't working this way then it maybe the typical issue I have found over the years with the difference between disc and digital games and is why I prefer digital 99.9% of the time. Somehow for whatever reason because the discs are hard coded sometimes the updates just clash with it and cause unexpected errors. It sounds like that is what is happening here as both my husband and I have played this mission through without errors since the day 1 patch and we both play the digital version of the game.
