- TIM brings Shepard back because he's smart and can see into the future and also likes taking the Shadow Broker's toys and knows she's the key to something to do with the Collectors and the reapers (oh yeah he made that connection)
- Finding the quarians on the colony Shepard is trying to save leads to TIM to go hunting and find out that the Quarians are planning an attack on Rannoch. He learns about Tali's mission on Haelstrom and has Shepard rescue her.
- Um. Stuff happens and the quarians go about their plans and Shepard is forced to intervene because TIM is all about wanting in on that and the council won't bother, figuring the quarians are just going to get themselves killed. good riddance.
- They do go to war and Shepard does make peace after locking Legion and Tali in a room together to work out their problems.
- But the peace is tenuous. There are a whole lotta geth and still many quarians who aren't too friendly about the idea of allowing them to live.
- So ME3 involves craaaazy Xen and her new geth (based on Tali's mission) and a faction of the quarians trying to destroy the geth (and throw in heretics in there somewhere) and they are the ones that have strapped legion up to this fancy new technology they found because these quarians are in fact indoctrinated and this is Harbinger's doing, having laid a trap for Shepard, knowing her strong connection to the quarian and geth but then Legion reveals that the reaper tech is changing the geth and war is going to break out again until shepard reveals that it's Harbinger doing this and they have to work together to stop him and and and..... oh oh your loyalty stuff from ME2 still plays heavily because it might mean that one or maybe even both of the fleets don't survive. Maybe they turn on each other or Harbinger just beats them if they don't join forces or... or... !
...needs some tweaking but yeah. canon.