In case you are all wondering how my guys seem to know exactly what's going on, it is all just educated guesses to them. 
It all revolves around the idea of Dimension 26, essentially Sub-Space. Through this dimensional corridor, it is possible for any ship in the R-Type universe to travel to emerge in any other dimension in any time. Through this, certain Space Corps ships can facilitate FTL travel through the use of warping through different dimensions. The Tesseract is essentially a man-made warp gate that allows for stable fast-travel throughout the Solar System.

Because of the instability of warping through time, space and dimensions, it is not entirely unlikely that it would be possible to stray into another timeline in the scope of the multi-verse. Though they don't technically have any proof of this, they have determined at this point that the Bydo had come from some future world in order to destroy mankind. [hider=Story Spoiler]Technically, this ends up leading into a closed time-loop in which an R-Type ship travels into the far future with a sample of the Bydo in order to warn the future humanity about it, but they blatantly don't listen and experiment on the sample until it grows into the Bydo Empire, destroys humanity in that time and goes back in time to do it again preemptively.[/hider]

So, yeah. Pretty much the train of thought here is that, "it's crazy enough to very possibly work that way."