Basically, it's this: right now, in the 1999 timeline, Umbrella is officially on its last legs. Linda and Yoko are testifying in the trial that will lead to its suspension of business decree, as per the start of RE4. That'll lead to the official end of the corporation as a legal entity, barring several last flare-ups (i.e. Dead Aim); Leon says in RE4 that Umbrella was "finished" shortly after the end of RE2, which implies its official end is coming.
In the 2006 timeline, Wesker is rebuilding Umbrella into a sort of shadow corporation that's a sort of front for illegal activity, as Ada notes in Separate Ways.
Basically, the STARS are being brought together in 2006 to combat the Umbrella of then, because the Umbrella of 1999 is already more or less dying on the vine.
Also, it's worth noting here that our 1999 and 2006 timelines are, as far as I know, the same world; they're just at different points on the same timeline. That's something that Will and I have been working off of since Claire and Leon met on Sages, back in the day.