One possibility would be to try using Panel in back of all tab contents and make sure the Panel spans the full size of each tab:
TabView[{Panel[
Plot[x, {x, 0, 1}, ImageSize -> 200, Background -> Green],
ImageSize -> {400, 300}, Background -> Green],
Panel[Plot[Sin[x], {x, 0, 19}, ImageSize -> 400,
Background -> Green], ImageSize -> {400, 300},
Background -> Green]}]