Well, think of it this way: imagine that you were trying to help someone else hack the Australian Department of Defense. Should you face an investigation and trial for it or are you immune because you're not Australian?
The US might extradite you if Australia could make that case. Especially if it could be proven that you would receive a fair trial and no cruel or unusual punishment. That's what's happening here. The UK can still refuse to give him up if they don't make a good enough case.
For context on the issue of "fair trial": look at cases of worse charges than conspiracy to hack, like Maria Butina, for instance. She still received a proper trial and chance to defend herself against the evidence. Our legal system is broken in many ways, but mostly when it comes to racial or income inequality and local law enforcement. On the larger stage the rules for these things are pretty clear.
If you want to see some contrast take a look around at other large nation's justice system.
If what I did is a crime under US law then yes, in the US. If what I did involved accessing servers in Austrailia, from the US, then again, only if what I did is a crime under US law then yes, in the US. If I claimed in an online chat that I attempted to derive a password from a hash and failed, while I was located in Mexico then no.
The idea of a government's authority being derived from a consent to be governed was expressed very early in the US of A's declaration of independence to Britian: "That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed" and I think this is a reasonable stance.
It sounds like you don't believe in extradition at all, but there is precedence for this and most western countries are on board. It's not just the US, UK, and Australia.
And the conspiracy wasn't just cracking the password, it was explicit intent to crack it for unauthorized access to classified military intelligence.
In limited cases I support it but I believe some type of consent to be governed is required, I consider physically visiting a sovern nation as implicit concent to be governed by their laws. I'm opposed to the notion that any government be able to determine the authorization for information access and excerpt authority on foreign citizens.
And that decision is up to the country who has him in custody, which is the UK right now. They've refused extradition for hacking before in the case of Gary McKinnon [1] due to fears that he could end up in Guantanamo so we'll see, now that Guantanamo is effectively closed for entry.
It's interesting that you present Butina's case as having been a fair trial. Her "crime" was basically naive, opportunistic networking with influential people (all of which was done publicly and even documented publicly on social media, so hardly consistent with a conspiracy). Hordes of people do that on a daily basis without registering as a foreign agent. But she's Russian, and in the age of Trump/Russia hysteria, that means you get selective enforcement of vague laws. Add a few months of solitary confinement and you arrive at a guilty plea.
The US might extradite you if Australia could make that case. Especially if it could be proven that you would receive a fair trial and no cruel or unusual punishment. That's what's happening here. The UK can still refuse to give him up if they don't make a good enough case.
For context on the issue of "fair trial": look at cases of worse charges than conspiracy to hack, like Maria Butina, for instance. She still received a proper trial and chance to defend herself against the evidence. Our legal system is broken in many ways, but mostly when it comes to racial or income inequality and local law enforcement. On the larger stage the rules for these things are pretty clear.
If you want to see some contrast take a look around at other large nation's justice system.