Yes, They ARE just making this up as the go along, but Mei's role isn't counter-canon.
Overwatch started as a 6-man strike team (And, presumably, associated support staff) to fight against the Omnic Crisis. After they succeeded, the organization Overwatch was founded as a general peacekeeping/humanitarian/"You saved the world now do what you want" group. In addition to combat teams they had scientists and the like. They were not just the Robot Fighters, (Although they did, illegally intervene against Null Sector in London).
That said, I've concluded that they were perhaps the most incompetent organization of all time.
Previously, we assumed that Mei and her team went under around the time Overwatch fell. They were forgotten amidst the chaos of the base exploding and everything falling apart.
But, now we learn that the Ecopoint team went to sleep nine years ago, four years before the fall of Overwatch.
Either the Ice Storm lasted 4+years, or people at Overwatch just forgot about what I'm guessing is a multi-million dollar research base (it's not cheap to build in Antarctica) with six staff members.
Even if the communications system was damaged by the Ice Storm, did they never send another supply drop? If they thought everybody was dead, did they not send a team to recover bodies and equipment?
Edit: As for "The Anomaly", Mei was a climatologist, at what we've been told was a climate research station. "The Anomaly" could just refer to some specific climate change based phenomenon that they were observing.