In the movie, immediately after seeing that Wade Wilson has mutated, Ajax makes a comment about his newly acquired regenerative powers. How did he know what the mutation was when all he could see was that DP was way uglier?
First of all, the timeline and how things progressed in the movie are not exactly the same in the comics.
In the movie, Ajax and his crew go out and search for people who are at the last years of their life due to lethal diseases. They offer them a way to cure themselves by injecting them a mutant gene. They knew he had terminal cancer due to his military records. His mutant side didn't come forward right away. They use extreme tortures on Wade to activate it. I think you already know this part.
Wade has terminating cancer. It has spread all over his body. By definition, cancer is irregular growth in body cells. When Ajax forced him to the edge, his cancer took over and started to spread everywhere. Since cancer made the cells faster in growth, this became his power. Deadpool has fast healing powers. This is the reason Ajax said he could cure him (was a lie) and why Wade went after him. Ajax knew what would happen.
It is about his cancer. This answer to a different question explains that.
In comics, learning that he had contracted cancer, Wilson broke up with Vanessa rather than force her to remain with a terminally ill man. In Canada, he was offered hope in the form of Department K, a special weapons development branch of the Canadian government. Wilson became a test subject in Department K’s branch of the joint U.S./Canadian superhuman enhancement project, the Weapon X Program; his cancer was temporarily arrested via the implantation of a healing factor derived from another Department K agent, the mutant adventurer Wolverine. Wilson was active in a covert field unit alongside the near-invulnerable Sluggo and the cyborgs Kane and Slayback. Vanessa herself was later affiliated with the team after having manifested mutant shapeshifting abilities, calling herself Copycat.
During one mission, Wilson killed his teammate Slayback. As a result, he was rejected from the Weapon X Program and sent to the Hospice, allegedly a government facility where failed superhuman operatives were treated. However, unknown to the Canadian government, the Hospice’s patients served as experimental subjects for Doctor Killebrew and his sadistic assistant Ajax, with the patients placing bets in a "deadpool" as to how long each subject would live. Killebrew subjected Wilson to various torturous experiments for his own deranged satisfaction. In due course, Wilson formed a semi-romantic relationship with the cosmic entity Death, who regarded him as a kindred spirit. Wilson’s emotional strength during his trials earned him the respect of his fellow Hospice patients. Then Ajax, angered by Wilson’s taunts, lobotomized one of Wilson’s friends. At Death’s prompting, Wilson killed his friend to end his suffering. However, under Killebrew’s rules any patient who killed another was to be executed; Ajax subsequently tore out Wilson’s heart and left him for dead, but Wilson’s thirst for vengeance was so strong that it jumpstarted his healing factor, regenerating his heart, although not curing his scarred body. Wilson then attacked Ajax, leaving him for dead in turn, and, taking the name Deadpool, escaped from the Hospice with his fellow patients.
More on Marvel.com: http://marvel.com/universe/Deadpool_(Wade_Wilson)#ixzz40vNJ6LE6
It is only my assumption, but I assumed Ajax didn't really wanted Deadpool to gain power when he putted him in the oxygen suppressor, just kill him slowly.
That explain why he meant by "calling it quit" if Deadpool didn t gain power, either he miraculously survive thanks to his power, either he dies, for Ajax, everything s fine.
Also, the effect it had on Deadpool's body indicated for me that he was not supposed to survive it, and Ajax simply had to jump to the obvious conclusion: if Deadpool survived, it s because he regenerate everything.