The concept involved here is extraterritorial jurisdiction--the US claims the right to enforce its laws on its citizens abroad in some circumstances. The most notorious uses in the US are FATCA (basically forcing foreign banks that do business with US citizen to hand information over to the US) and the FCPA (allowing anyone with pretty much tangential relationship to the US to be sued for bribery). It's telling that the FIFA corruption scandal was brought, not by any EU courts, but by the US federal prosecutors.

In these sort of situations, the main thing that tends to apply is not the ability to get a judgement in court but the ability to get that judgement enforced. So if, say, Fiji were to make up a law and convict, say, Donald Trump under it, no one would care--Fiji would have no practical way to enforce that judgement. But the US can generally get its judgements enforced, even outside the US.

In the specific case of the financial world, the size and importance of the US financial markets gives the US unparalleled power to enforce judgements. The US could not only lock you out of dealing with USD transactions directly, they could also direct banks that do business in the US to not do business with you.