They flew those, but were more closely associated with the P-51. The planes in the trailers appear to be the P-51D variant, which I what I've always associated with the Red Tails.
If my memory serves me correctly, the Tuskegee Airmen started out flying Curtiss P-40 Warhawks...
Then briefly with Bell P-39 Airacobras...
Very briefly with Republic P-47 Thunderbolts...
And finally with North American A-36 Apache (listed in some sources as "Invader") the ground-attack/dive bomber version of the P-51...
And finally with the P-51-D Mustang...
But then again, why quote history... when Hollywood and George Lucas knows best?