Over the past two days we learned once again, that Twitter isn't secure. This shouldn't change anything for the Brand Marketers of the world.
Brand Marketers don't share private data on Twitter (or at least, they shouldn't be). Users aren't going to leave Twitter overnight and neither should you.
However, if you did receive private account data in a Direct Message, you may want to reset security on the account. This is probably unnecessary, but a smart security gesture.
Now, what if something even more damning comes out over the next few days and users actually migrate to a new platform? Nothing changes. Real social success in Twitter comes from conversational relevance. This relevance will continue wherever users migrate. You may want to run a promotional gimmick to remind people that you are there, but your value won't change all the much.
Because your value is not in the platform, but in the quality of the connections you make. Continue to use Twitter for what it is, a tool that enables conversations. So go ahead and talk. Nothing's changed.