This is a great point. If a normal criminal law were at issue one might say it would not have jurisdiction over acts that took place outside of their state. But since the law is enforced by private citizens they can file suit and a Texas Judge will decide whether their courts have jurisdiction.
I think your post brings up issues covered by the privileges and immunities clause of the constitution because such an application of the law would impede interstate travel (briefly covered in the second to last section here).
https://en.wikipedia.org/wiki/Privil...unities_Clause
I believe the Supreme Court will eventually hear these cases. While the law itself will deter abortion providers, someone will eventually sue and the Supreme Court will be able to hear the case because the defendant can appeal it to higher courts once it is enforced. As the vox article points out, simply violating the law so that you can challenge it threatens you with bankruptcy because of how many suits can be brought against you.
Another problem I have with the law is that by providing for civil lawsuits to enforce the law it evades the principle of standing for judicial cases. The standing requirements basically ensure that someone who is suing (in a civil action) is the actually harmed or aggrieved party in a case and that the issue can be redressed by a favorable decision. The standing requirement is a constitutional requirement that applies to state courts as well and is embodied in the "case or controversy" clause in the federal constitution. It is inconsistent with these principles to say that a random person is the aggrieved party when someone violates an anti-abortion law.
The issue as the vox article pointed out is that Texas came up with a novel way to frustrate challenge by not having the attorney general enforce the law. I would say the law would be overturned when it gets to the Supreme Court (on a number of grounds) but all bets are off with this court.
