The TEC commentator is talking about how they just allied with the Vasari Rebels. He's saying that alliance could save them, especially if the warning from the Vasari (implies they finally told the TEC everything about why they're running) is true, because that means there is some unknown and potentially unbeatable enemy following them. Hence the Vasari Rebels are their salvation because otherwise they wouldn't know to run (the fact they are jumping to a new solar system at the end seems to imply the TEC Loyalists and Advent Rebels all run with the Vasari Rebels like the VR wanted, but that will probably only technically take place in a sequel).

So no, you don't really need to know anything else in the lore, its just a really condensed trailer so you have to read between the lines.

Actually, I think the Vasari Rebels want to settle and believe they need to ally with the Advent and TEC combining their strengths in order to make a stand when the unknown threat catches up with them.  Which either they believe is inevitable and believe their best chance of survival is to ally with the other 2 great factions, or they are just tired of running and would rather stand and die fighting.  It's the Vasari Loyalists that are dead set on running away, which is why their tech allows them to completely uproot and strip and get back on the run as soon as possible.

But then again, I don't know for sure... Hopefully we'll get hard answers someday.

If you want, you could download the manual for Sins Rebellion by going into Steam Library -> Right-click Sins Rebellion -> Select "View Player Manual".  It will open a PDF web page which you can download.  Starting on page 5. it tells you the full back story of all the races in the game.  Starting with TEC, then Advent, and then finally Vasari.  It's a good back story and interesting read.

Hope this helps.