As I understand it, that's just wrong. You can be subject to U.S. law if you commit a crime in any U.S. territory (this applies to all countries, not just the U.S.). Since Assange is being charged with conspiracy and the Americans say they have evidence that he did not just receive information from Manning, but helped to direct the hacking and theft of confidential documents, Assange may have exposed himself to legal repercussions.
Now, I'm not a lawyer, but it seems to me that there is a legal distinction between a journalist who publishes classified information that was delivered to him without foreknowledge of or participation in the crimes committed to gather the information, and a journalist who directs and aids in the crimes committed to gather the information. In the first case, the journalist is merely carrying out his duties as a journalist and should be fully protected by the first amendment. In the second case, he has actually committed several crimes that the first amendment will not protect him from, thus the espionage and conspiracy charges.
Now, I can't say whether Assange actually did any of the things that the U.S. Justice Department claims he did. However, if he did and either Manning or the computer that Manning "hacked" were on U.S. soil at the time it was "hacked", then Assange committed a crime on U.S. soil and he would rightfully be subject to U.S. jurisdiction and U.S. laws related to that crime and could be legally and reasonably extradited to the U.S. to face those charges.
On the other hand, I think the 18 charges with a 10 year sentence each is entirely unreasonable and the Trump Justice Department is obviously looking to destroy Assange because they can, and because Trump's voter will probably love seeing Assange destroyed. Most of them probably already think Assange is a traitor and should be executed. Now that's obviously stupid and wrong, but most Trump voters don't seem to care about that at all.