As an aside. I have seen some historians mention some of the other larger European wars in the modern period as being "World Wars". I have seen some comment on the Napoleonic Wars, The 7 Years War, the 30 Years War, and The War of the Spanish Succession as "World Wars" since these wars had fighting globally to some extent. These were all after the fact and did not have contemporaries making such claims, as far as I am aware.

This has been asked and answered before, more or less. In reference to what we now know as World War I, that war was first called the "World War" by the newspaper the Pittsburgh Press on August 2, 1914.

American newspaper articles routinely called the conflict a "World War" while it was still ongoing, as typified by publications of columns from the St. Louis Globe-Democrat and New York World.

The first time it was called the "First World War" was probably by Laurence Stallings' 1933 photography book "The First World War" which was kinda/sorta turned into a movie of the same name the following year. The film, in fact, was comprised of silent newsreel footage of the war narrated by author Stallings.

As for WWII, the Oxford English Dictionary says that the Manchester Guardian used the term "World War No. 2" in an article on February 18, 1919. The first time the actual conflict that became known as WWII was referred to as the "Second World War" was in Time magazine on September 11, 1939. From there, "World War II" began being used later during the course of the war.

So to answer the question, "When were they considered 'world' wars?" During the course of the respective wars.

The terminology changed from "World War" --> "First World War" occurred in the 1930s, and "Second World War" --> "World War II" during the course of WWII, at which time "World War I" was also adopted.