There's two things involved. First is a delay before the Lodestone (and therefore the forums) updates your character's data. There isn't much you can do about that part.

But then, even if the Lodestone has an updated picture, your browser might have an older one in its cache, in which case you might still be seeing the old image even when other people who didn't have it cached see a newer one. If you think it's the later (like if the forum shows a different image than the Lodestone's full page for your character), then try clearing cached images from your browser and refreshing the page. (Or just wait. Eventually, your browser will decide that cached image is too old and will pick up a new one.)