Here is how conservatives judges, such as Justices Scalia and Thomas, interpret the Constitution. If the language of a statute is unambiguous, the courts will use the “plain meaning rule”, interpreting the words of the law according to their ordinary everyday use. In that case, legislative intent is irrelevant.
The word jurisdiction is well defined by the courts. In law school, it is the first concept introduced in Civil Procedure and takes about three weeks of instruction to cover it. It is the power of a court over a person or the subject matter of the lawsuit. Your presence in a state is considered consent to being subject to its laws. Simple as that.