It's retroactively implied, as Earth is not explicitly named in Transdimensional Maneuvers, but it is in SOTS and Tertiary. So, while Cyclone and Kate getting stranded on and rescued from Earth are effectively canon now, any other details of the circumstances of the event are not necessarily canon or true, and should not be presumed to be, as the sequel trilogy is not considered canon in any dimension.
This is not to be confused with the original version of Full Circle which is considered to have taken place in the Future Dimension with the Darkitect being killed near the end, ending the war shortly after, creating the world that the Figdroids takes place in.