is there some tax rule stating that things change?
There isn't. US citizens are required to report their worldwide income to the IRS, and to figure their tax on the basis of their worldwide income, no matter where they live.
If the states' secession is recognized by the US government then there would be a negotiated agreement with terms governing all sorts of things that need to be taken care of in connection with that secession, not unlike the negotiations currently under way between the United Kingdom and the European Union. (There would probably also have to be an amendment to the US constitution.) In that case, the answer to this question would depend on the outcome of those negotiations. Presumably the negotiations would include some mechanism for the residents of the states leaving the union to lose their US citizenship, along with changes to the Internal Revenue Code.
If the US does not recognize the secession then there won't be a secession. The states would not be able to deploy sufficient military force to assert control over their territory. The US citizens in those states would therefore remain US citizens, liable to the IRS.