The Triverse is comprised of three linked worlds - Hearts, Innocence, and Tempest, that are connected through the Triverse Gates. Gall, QQ and Kongwei are recurring characters and inter-dimensional travelers that either "travel in time" or "travel through memories". It is assumed they are all originally from Tempest's world.
In Tempest, King Areulla VIII uses a strange, experimental magic to hurl himself through space, landing in Areulla. He builds this power and opens a portal, hinted to be the Triverse Gate, to his home world.
In Innocence R, the Triverse Gate shows a bunch of visions of the Hearts and Tempest worlds while the party is traveling though it. QQ and Kongwai already know of the events of Innocence, which are considered legends in their world. There is a scene where QQ tries to intervene and rescue the party from being captured, but Kongwai stops her saying they're not allowed to interfere with the course of the story. Kongwai also already knows who Ruca is when they first meet, and he already knows the two people whose souls he has to save. He also knows who will betray the party and makes cryptic allusions to that.
In Hearts R, Gallando is stranded/considered missing. QQ and Kongwai are the only explorers to have ever safely made it back. You can see QQ in Hearts R secret ending, and the soldiers are clearly surprised that there's a survivor, Gall, coming from the Gate.