The first waves were not of anatomically modern humans but Homo erectus and its contemporaries up into modern Georgia, then East into China, then eventually into Indonesia.
Then around 1 million years later, there was another migration of Homo erectus out into Southeast Asia along the coast through India and eventually into Vietnam and Malaysia.
This second migration seems to be what the paper is referencing and definitely the one that, at least 10 years ago, the anthropology community had the least confidence in. My understanding, again dated by a decade now, is that it was uncertain if hominoids entered Europe at that point or not.
Neanderthals left Africa 500,000 years later into Europe while Denisovans left at the same time into Asia ending up concentrated in Serbia.
Modern Humans don't show up until another 400,000 years after that (around 100,000 years ago) and don't leave Africa until 70,000 years ago. They also left Africa in multiple waves with 5 main ones spreading out across the globe.