The paper doesn't actually mention anything about cities being that old. As for agriculture, it's really talking about the translocation of plants and a few animals from island to island in Melansia that occurred between 45k and 25k years ago. People in that region were manipulating their environment and spreading essential food species around (like yams, sago palms, and cuscuses) very early. That's been known about for at least a decade, so this isn't earth shattering information for people familiar with the archaeology of the region. This wasn't full blown domestication of plants and animals though, and the article still references mid-Holocene Kuk Swamp as the earliest evidence for that in the region, between 9k and 6k years ago depending on the species of plant in question.

The main point of this article is to demonstrate with these examples that humans were manipulating their environment in fairly significant ways that don't involve overt agriculture early in our collective history and, hypothetically, could have been manipulating the environment in similar ways earlier on that we haven't detected yet and should look for, just in case. It's fairly easy to tell that humans are moving plants and animals around between islands where those species couldn't have reached otherwise; it's harder to tell when this is happening in, say, tropical Africa.

After discussing these early examples of human manipulation of tropical environments, it continues on discussing later developments - like the aforementioned Kuk Swamp site in Papua New Guinea, the rise of tropical civilizations like the Maya in Mesoamerica and the Khmer in Indochina, the spread of agricultural Bantu cultures through tropical Africa, and the development of terra preta-based agriculture in the Amazon, all things within the last few thousand years - not tens of thousands of years.

The other linked article, from arstechnica, seems to be lumping all those events into one sensationalist ball to talk about lush Garden Cities in the tropics 40,000 years ago. So the fault lies there, not with Nature.

I would like to point out something pertinent to your reasoning, though not to ancient agriculture. Things published in Nature are actually MORE likely to be incorrect; this journal is known to have an elevated rate of retractions as compared to field-specific journals.