Travis-CI badge not updating
Not sure about Travis-CI, but I know GitHub aggresively caches images. Once the cache goes stale you'll see the correct badge. Other than waiting there's not much you can do.
The previous answer is so close! Github wouldn't be involved at all, all they do is link to the image with html. And I know from experience that Travis updates it basically immediately. It's actually browser side caching!
Your browser doesn't request the new image because it already has it. This is actually how all images work on the web. You can rest assured the correct build status is showing for new visitors to your repo.
If you need that green badge to show up for your own peace of mind, just hit Ctrl+F5 to purge the cache.