The substance dualists whom I have read address this question do so by denying that there are two selves. This argument relies upon several points:
1) The family of the split brain patients, as well as the patients themseves, report that they are one integrated self, not two. Any division may then be an exotic artifact of the experimental setup, not an actual split.
2) These "selves" are not co-equal, the secondary ones are generally non-verbal. It may be an unjustified inference that they are both selves. In the experiments conducted, there may only be one real self, plus an automoton that has no inner life.
The dualists who advocate these arguments generally believe in the unity of a self, hence their dualism requires them to deny even strong evidence of the modular nature of selfhood.
Some dualists have instead advocated that all humans have two selves. https://www.cambridge.org/core/journals/behavioral-and-brain-sciences/article/case-for-mental-duality-evidence-from-splitbrain-data-and-other-considerations/CCC275C97E2E658D56F9BF3CA7463DE4
Here are three references that will help point to how this question is addressed. Nagel points out the problem is not just a problem for dualists -- it is not just dualism that concieves of consciousness as a unity, pretty much all people who accept the existence of consciosuness do: http://www.oswego.edu/~delancey/100_DIR/Nagel.BBUC.pdf
This link discusses further some of the materialist use of these experiments, and a variety of dualist strategies in addressing the materialists: http://www.oswego.edu/~delancey/100_DIR/Nagel.BBUC.pdf
This third link focusses more explicitly on the dualist responses, and their validity. Note that Nagel is a property dualist, and the other two links discuss several variants of dualism, not just substance dualism. This third link, by quoting extensively from Eccles, provides the most extensive substance dualist discussion. https://uncommondescent.com/intelligent-design/do-split-brain-cases-disprove-the-existence-of-an-immaterial-soul-part-two/
There are not a lot of substance dualists developing the theory, and I have not seen any offer the model I think is most consistent with this evidence. This model is:
a) selfhood, and willing, are products of the spirit
b) in early life -- spirit ensouled proto-life, and provided awareness, processing, and willing functions which early life had not developed chemically, and this gave ensouled protolife a massive evolutionary advantage over any that were not ensouled.
c) as life became more complex, the throughput of spirit to guide a living entity was insufficient, so evolutionary processes lead to much of the actual processing offloaded from spirit to chemistry.
d) As life continued to get more complex, even much of consciousness was partially offloaded and/or amplified by chemistry.
e) this leads to unconscious neural modules doing functions which COULD be separated from the consciousness, per 2) above
f) or the possibility that more than one spirit could ensoul bits of a neurology, particularly if that neurology is no longer self-integrated due to being sliced into separate pieces.