I originally intended Arena Battle, my first RP here and my first RP ever, to just be a simple one-off. And it originally had a much simpler concept than what actually happened. It was just supposed to be exactly as described on the signup topic.
But as the RP progressed, so too did my ideas for its story evolve. I decided to create a conspiracy and include a shocking plot twist at the end of the RP. But I still intended for this to be a one-off.
Then when Majestic League's signups were released, I decided that I wanted to continue the story of my characters from Arena Battle and further develop them. But I didnt really intend for the two RPs to be connected.
When I Unexpectedly became the GM of Majestic League, I had now assumed full creative control. And I decided that I in fact did want to connect this RP to Arena Battle. And it was only natural, since 3 of Arena Battle's PCs besides my own had also returned for this RP as well.
And in addition, I had begun to develop the idea for a more direct sequel to the Arena Battle RP. So I decided to link the end of Majestic League to the beginning of this new RP, "Death Race". Abd some of the Majestic League characters(Hydron and Sadie) had come along as well.
At the same time, I had also been running The Last Resistance RPs, which originally were only semi-Canon to my other RPs and not meant to be crucial to my main stories.
I had originally intended to return Death Race's party all back to earth at the end of Majestic League's sequel, "Majestic League VOL 2". However due to internal conflict the RP had been canceled.
So I decided to make a last-minute improvisation and start my own originally-created Superhero RO series: 2059.
And what's more, was that some of Majestic League's players had also returned with their Majestic League chatacters too, and eventually nearly all of Majestic League's players had returned.
It was at this point that I finally had a clear vision of what I wanted to do with my RPs and what direction I wanted to take. And that was to make one large interconnected universe with spinoff RPs that took place in various different time periods.
And 2059's sequel, 2059: The Incasion, was the one RP that finally officially cemented my Universe as being a universe.
And well, the rest is history.
TL;DR it basically just happened on its own.
I don't think they explicitly did, but I did clarify in the RPs' signups that they were part of a larger universe as well as what point on the timeline they took place.
And the fact that the same players almost always returned, and that they had reoccurring characters of their own and that they were willing to work with me showed that they were interested and invested in my concept.