There are no "kinks in the system".
The idea is that the law is the law, no matter which court is making the ruling. If the president is in violation of the Constitution, then any judge has the authority to stop it.
They can appeal that decision if they choose to, but it's not like there are some judges that are allowed to determine what's legal, and others that aren't. If the order is illegal, it should be stopped as soon as possible...not weeks or months later, when the Supreme Court finally gets involved.
The Constitution does not support that school of thought. It is very clear, that the rights it affords are universal and apply to everyone in the country. It says nothing about being a citizen or not.