I'm not quite sure I understand your question so I'll just answer as I can: Crimes committed here are tried here or to put it another way for example: if you commit a crime in Houston, TX, you will be tried in a court in Houston and if you are convicted, you will then serve your time in a prison in Texas, or wherever and how ever the judge decides after the conviction. The local and federal authorities don't like to send people accused of committing a crime in their jurisdiction to somebody or somewhere else to be tried and punished. You will most likely be deported after you have been convicted and have served your full sentence here. The only way you can be tried in another jurisdiction (like another city, county or state, would be if the judge decided you could not get a fair trial in the area where the crime you are accused of was committed. This very rarely happens, though.
If you have committed a crime in another country and then fled here, the country in which the crime was committed can request that you be extradited, or sent back to stand trial there. If the US has an extradition treaty with the country, you will be arrested here and either sent back to that country under guard until you are handed over to the authorities in the other country, or they may send their own authorities here to take you back under their own guard.