So, what is the right approach? Start the extradition process when you don't believe the individual is guilty? I would hope not. Taking action to bring someone to trial because you believe they are guilty is entirely different from the claim that in the US you are now "guilty until proven innocent".
Presumption of innocence means that the burden of proof is on the prosecution in the trial. It does not mean that the prosecution is required to not believe themselves that the individual is guilty.