Was the twist in the 75th Hunger Games predetermined to send the victors back in, or was it changed by President Snow when he needed a way to get rid of Katniss? The Quarter Quells are the only Games that are different. This is convenient since the President needs one.
It is unknown whether Snow changed the plan for the third quarter quell to send Katniss back into the Games but it is likely that he did.
A great number of the games were planned at the outset of the creation of the Hunger Games, including the concept of the Quarter Quell having an extra twist, but there's no information, either in the films or in the books that definitively say whether what occurred in the 75th Hunger Games was the plan or whether Snow changed it.
One point made in the article argues that it's unlikely that it was planned from the beginning... there was no way the founders could predict that there would be appropriate candidates for the games if this were the case. Until Katniss won the 74th Games with Peeta, there was no living female Victor from District 12, and it's unknown whether there had ever been one at all:
We don't know conclusively, but it's almost certain that the 75th Games (which were planned) were altered to include former winners so as to kill off Katniss (and subdue the rebellion).
I think you've answered your own question.
In Catching Fire, following Katniss and Peeta's victories, frustration among the people is growing. They have seen two people defy the Capitol and Katniss in particular is becoming a symbol of rebellion.
Snow wanted Katniss and Peeta killed at the end of the Hunger Games, for their "stunt" with the berries. But Seneca Crane instead announced them as winners (and paid for it with his life). So now Snow is aware that both Peeta and particularly Katniss are symbols, and a threat. The film echoes the book in this regard, and to quote from the book:
So at this Stage, Snow wants Katniss on board. He is hesitant to kill her, as it will stir rebellion - but he can't let her "go free", as she will stir rebellion. So he wants her to behave well and do as he says.
Of course, this fails. She pays tribute to Rue in District 11 and sparks visible dissent. A man in the crowd is shot dead and tension is clearly rising.
At this point, Snow is even more concerned. Something the book mentions, which the movie does not, is the following scene which takes place in the mayor's house (during her tour of the districts):
So there is full rebellions occurring now, across all of the suppressed districts. Snow's plan of keeping Katniss "on-side" has failed. Inadvertently, through her tributes to Rue and simply by her being strife is brewing and more signs of dissent are breaking out.
This is when Snow hatches the master plan to send Katniss back into The Hunger Games.
Katniss realises that she'll likely die from this:
Now, at the start of the Catching Fire novel, Effey tells Katniss "In your very first year of being a victor, you get to be a mentor in a Quarter Quell!”
Our only knowledge of a Quarter Quell comes frmo a recollection Katniss had:
So we know the Quarter Quell is designed to be special. But given Effey's comments, and the knowledge that former winners are supposed to be exempt it seems almost overwhelmingly likely the rules were changed so as to trap Katniss in a situation where she could be killed without sparking further unrest.
We don't definitively know. There were going to be Hunger Games that year. But it's overwhelmingly likely that the Games were altered to include Katniss.
Some good answers before this one but all of them sidelined one crucial detail or rather person: Plutarch Heavensbee (RIP Mr Hoffman)
After Crane was killed due to the debacle of 74th Hunger Games, we see Plutarch being appointed as head Gamekeeper and a very close associate of President Snow. Plutarch was giving an angry and anxious Snow valuable feedback and advice on how to tackle Katnis and defuse the uprising.
It is only later we find out that Plutarch has ulterior motives in being so close to Snow and the Games itself.
We also find out that most of the tributes of 75th Hunger Games, all of them being previous Victors, are in on his elaborate plan. It is highly likely that the plan was brewing much before Katnis came on the scene, much before 74th Hunger Games. Because forming an alliance will take much time and effort and trust. They all were waiting for a right time and a right person to galvanize their fight against the Capitol. And since Katnis served that purpose perfectly, Plutarch must have decided its time to implement his plan.
Plutarch knew Katnis enough to know that she was impulsive and brave even under mortal fear. He knew the Victory tour would not go according to Snow's plans, which were suggested to Snow by Plutarch himself. To paraphrase "Distract people with the wedding. Show her as one of us now. They will hate her so much, they might just kill her for you"
So, it is more likely that after Snow's plan, mentioned above, failed. Plutarch convinced Snow that the right way to kill Katnis would be under the guise of another Hunger Games rather than shooting her on point-blank. And since 75th Hunger Games were Quarter Quill, they had a disguise for their plan.
So, it is most likely Plutarch's idea to have Victors as tributes to the 75th Hunger Games and since most are in on his plan, and were ready to sacrifice their life for Katnis's safety, he knew that his plan would work. So he manipulated Snow's decision