No, US citizens do not lose their rights to a trial because they're not in the US.

I know this is what you're saying but just to head any other knee-jerk responses, US citizens do not lose their rights to a trial in the US, for breaking a US law, because they happen to be outside of the US.

Relatedly, when the question is "is this person protected by the Constitution," imagine a Venn diagram where one circle is "US citizens" and the other circle is "human being physically present within the United States." Debate over the 100-mile "border zone" notwithstanding, the entire thing is filled in. If you are a US citizen anywhere, or a person inside the US, you have all the Constitutional rights.

It does change whoever might have standing to sue the President over it, let alone to put him in jail.