I'm still not sure if I understand what you're asking for, or whether my comment above provided it, but having just finished reading Articuno's link to Meads v. Meads, I figured I'd quote from it to flesh out my comment.
You say you are looking for "evidence", but it's unclear what kind of evidence you will accept, since the word can mean at least two different things. I'll attempt to elaborate on each.
Evidence from examples
I'm not going to go into significant detail here unless you ask for it, but I will point to speeding tickets and licensing for out of state marriages as two examples of cases where the laws where you are currently located take precedence over the laws where you come from.
Specifically: If you're going 10 MPH over the speed limit in a state where the fine for that is $500, it doesn't matter if the state you're licensed in would only fine you $10 for that, or even wouldn't bother ticketing you at all. You're still liable for the $500 ticket.
Likewise, if you're in a state which requires a three-day waiting period between applying for a marriage license and getting one, or between getting one and when you're actually allowed to get married, you're still able to go to another state which is willing to issue same-day marriage licenses to out-of-state couples, get married, and return to your home state before you would have been able to get married if you had stayed.
Evidence from justification
In Meads v. Meads, Justice Rooke says:
I have reviewed, in my discussion of the inherent authority of superior courts, why everyone who is in Canada is subject to Canadian law and the Canadian courts. Further, this is a simple fact known by all, an element of the most basic levels of education, and a cornerstone of the operation of an ordered society. [Para 568]
In the "discussion of the inherent authority of superior courts" section, he writes:
The courts in Canada are a separate, distinct, and independent branch of government. In [previous cases, it was] concluded that the independent character of this and other Canadian courts flows from unwritten constitutional principles that have been inherited from the U.K. and are a separate and essential constitutional aspect of government, "definitional to the Canadian understanding of constitutionalism".
The authority of this Court, like other superior courts of inherent jurisdiction, does not flow from legislation, as does, for example, the Provincial Court of Alberta. Rather, this Court has inherited that jurisdiction as a successor to the English Royal Courts. [A previous case] explains this Court's genealogy:
... The provincial superior courts have always occupied a position of prime importance in the constitutional pattern of this country. They are the descendants of the Royal Courts of Justice as courts of general jurisdiction. ...
That heritage reaches to the very foundation of an independent judiciary:
... "Superior Court" is to be construed historically, and that ... it connotes a court having an inherent jurisdiction, in England, to administer justice according to the law, as and being a part of, or descended from, and as exercising part of the power of, the Aula Regia, established by William the First, which had universal jurisdiction in all matters of right and wrong throughout the kingdom, and over which, in its early days, the King presided in person.
In other words, because the King had jurisdiction over everything in his kingdom, and he designated courts to handle cases for him, then the current iteration of those courts have jurisdiction over everything within their areas. This holds true even if the current iteration is no longer appointed by the King (or Queen, in this case) directly.
Similarly, for countries which don't have a monarch, universal jurisdiction is invested in someone or some body. In the US, that's the Supreme Court, but in other countries it could be the legislative body or the head of the country. Under that level (whatever it may be), lesser courts handle subsets of the case load.
As for why there has to be some body which has universal jurisdiction over a country, I'll cite Justice Rooke again:
A superior court of inherent jurisdiction has a special general jurisdiction in substantive as well as procedural law. It is a clear and well‑understood principle of Canadian law that where a person has a right in law, there must exist some tribunal where that right may be exercised and defended. If no other court has been assigned authority to address a particular kind of legal action or subject matter, then that authority falls to the superior courts of inherent jurisdiction.
The Supreme Court of Canada considered this inherent substantial jurisdiction of provincial superior courts in Canada (Human Rights Commission) v. Canadian Liberty Net, 1998 CanLII 818 (SCC),  1 S.C.R. 626 at para. 32:
The notion of "inherent jurisdiction" arises from the presumption that if there is a justiciable right, then there must be a court competent to vindicate the right ... the doctrine of inherent jurisdiction requires that only an explicit ouster of jurisdiction should be allowed to deny jurisdiction to the superior court. [Emphasis added.]
Again, to rephrase: If you have a right, there must be something to ensure nothing infringes that right. Thus, with no ultimate court, there's no inherent rights to preserve, because every "right" you have can be infringed on at will (by someone, even if not by everyone).
In short: "Yes, there is evidence"