What is likely meant is that the 1918 H1N1 pandemic flu could progress from the onset of severe symptoms to death in a matter of hours, which is a very different prospect from progressing from initial exposure to death in hours.

In any event, the 1918 pandemic flu did not kill everyone it infected, it had a mortality rate somewhere in the range of 3% to as high as 10%. Even at the upper end of 10% that still means that the majority of people who were infected would survive, and many of them would experience comparatively ordinary flu symptoms and spread the flu around as it normally spreads.

In modern times the world is tremendously interconnected on a global scale. Almost anywhere on Earth one might come into contact with a traveler who has recently come from almost anywhere else on Earth within the last day. And, of course, the global economy is built on a backbone of international trade and logistics supply chain that stretch around the globe. Even a tiny company might have offices in multiple continents, and small scale manufacturers might have production in one country, assembly in another, headquarters yet elsewhere, and so forth. This, of course, also makes the global population extremely vulnerable to disease transmission. Most individuals anywhere in the world are not globe trotters, but enough are that it's almost impossible to stop importation of disease.

However, this is mostly a difference in degree rather than a difference in kind compared to historical norms. Extensive long range travel and trade, spanning continents and even sometimes oceans, has been ubiquitous throughout civilization at least going back to the Bronze Age. As has, of course, the spread of diseases across interconnected regions of the globe.

While travel was slower and less ubiquitous in 1918 it was still quite prevalent, especially as there was a significant amount of movement of people due to the war (naval crews, merchant mariners, military personnel, and refugees). That was more than sufficient to seed the infection across every continent and in the majority of populous countries, and from there shorter range transmission chains caused the bulk of the spread to the majority of the population.

There is one other major important factor here as well, and that is secrecy during the war. During WWI almost all industrialized nations were engaged in the war, and almost all of them relied on extensive censorship and propaganda campaigns to bolster the war effort. That meant hiding the true cost and inhumanity of the war from the public, and it also meant hiding inconvenient and demoralizing news related to the war as well. Which also extended to suppressing news of the flu. We don't have enough data to pinpoint the origin of the 1918 H1N1 flu strain, the reason it's called the "Spanish Flu" is because Spanish newspapers were the first to report on it, being unfettered by the censorship common throughout the rest of the world, since Spain was neutral during the war. Partly because of that censorship much of the world was in the dark while the flu was spreading among the population.