This isn't quite correct.

First, DDT was actually not globally banned for disease control and still isn't. What was banned was the indiscriminate broadcast spraying for agricultural pest control. DDT is still used in local applications on thatch and other rough surface walls where its excito-repellent effect (insects find contact with it irritating) keeps insects away with much less chance of developing local resistance. This disrupts the transmission chain between people and mosquitoes in both directions.

Second, for most purposes it has been replaced with pyrethroid insecticides, largely due to resistance concerns.

Third, the malaria case-rebound in the 1960s was indeed due to premature discontinuation on interior residual spraying programmes but that had nothing to do with a ban on DDT (still used for this purpose today) and everything to do with errors in data evaluation.

Previous eradication campaigns in Southern Europe and the US had been based on a combination of source control (draining swamps, removing breeding locations near dwellings), improving agricultural worker housing with treated nets, window mesh etc., education about the dangers of being outside at dusk unprotected, personal mosquito repellent, and chemical means such as IRS of interior walls with DDT and larvicides in remaining stagnant water. In addition, chloroquine became cheap and widely available through the 50s and this meant that people spent much less time at high infection levels where they were able to spread malaria back to mosquitos. Chloroquine resistance developed later.

Once this led to a substantial drop in malaria prevalence, the model switched to a medical one of case surveillance and isolation. In most places, humans are the only malaria reservoir (there is some disagreement as to whether there are relevant animal reservoirs in parts of Africa where malaria is holoendemic. The CDC says that humans are the only reservoir for malaria, I'm not sure that is definitely true everywhere but on the other hand I don't know as much about malaria as the CDC does.) so keeping humans from spreading it to mosquitos will work once you've knocked down the mosquito reservoirs enough.

This worked very well and led to widespread eradication success in much of the world. It did not work in India and Sri Lanka and was never even attempted on a sufficiently large scale in Africa (in parts of South Central Africa the prevalence was and is nearly universal so the threshold required for local eradication is higher than in places like Florida and Sardinia where it was an occasional disease of agricultural workers). Why did it fail in India and Sri Lanka, despite the fact that DDT continues to be produced and used for vector control there?

They switched to the medical treatment phase based on incomplete data. This switch didn't happen in other places until virtually all properties had spent several years receiving IRS and other steps had been in place for years, by the time that IRS stopped there was essentially no transmission of malaria. In Sri Lanka, they stopped it at a predetermined prevalence number but we later found that real prevalence was probably much higher than that.

Sardinia is a useful comparator. First, it is a moderate sized island so once cleared it can stay cleared with cheap countermeasures. Second, the "eradication programme" which lasted from 1946 - 1950 was enormously expensive (in the summer of 1948 as many as 30,000 people worked on drainage and brush clearance) and didn't actually manage to completely eradicate anopheles anyway. Such a programme was possibly only by external funding (essentially as part of Cold War manoeuvring over political control of Italy). Third, this came only after decades of pre-war investment in other measures to reduce malaria on the island. Between 1900 and 1914 alone, malaria mortality was reduced by almost a factor of 10 and the interwar governments undertook substantial drainage programmes which further reduced breeding locations for Anopheles.

The claim that the DDT ban led to millions of deaths therefore depends on:

-There being a ban, which there is not

-The counterfactual of a Florida/Sardinian style combined arms campaign including DDT and completely wiping out malaria but being made impossible only by the lack of DDT which is also not the case.

People often counter the claim with a correction to only the first point but the second is at least as important.