The Radio Show in 1930
In the 2nd or 3rd episode of the 2nd season Harper (born about 2008), impersonating her great grandmother Daisy Tremont (born c. 1918) in the year 1930, talks to her great grandmother's younger brother Sam Tremont about his favorite radio program, about a time traveler.
I am not an expert on the history of radio, but I know a bit about the history of science fiction.
There were various 19th century short stories and novels that can be considered science fiction, and there were an increasing number in the late 19th and early 20th century. Weird Tales, the first magazine dedicated to horror ficitn and fantasy fiction genres, began publishing in 1923, and the first magazine dedicated to the science fiction genre, Amazing Stories started in 1926, just 4 years before 1930. The first science fiction comic strip to bring science ficiton ideas to a whider audience was Buck Rogers in 1929.
The first popular English language novel about tme travel was The Time Machine by H.G. Wells (1895), which greatly popularlized time travel and time machines.
https://sf-encyclopedia.com/entry/time_travel
So creators of radio shows could have heard of time machines and time travel and decided to make a radio show about a time traveler as early as 1930. But that seems early to me.
So maybe The Secrets of Sulpher Springs happens in an alternate universe where science fiction books, magazines, comic strips, and radio programs became popular earlier than in our history and popularized science fiction ideas earlier, thus explaining why Sam is so influenced by science fiction in 1930.
By the way, I wonder if Americans began calling World War One by that name as early as 1930.