The US has jurisdiction because you committed a crime in the US. Canada has jurisdiction because you committed a crime in Canada.
As added complications, if you are a Mexican citizen then Mexico has jurisdiction and if your victim is Chinese then China has jurisdiction. If you get arrested on an Interpol warrant in Spain then Spain has jurisdiction. And so on ...
Your implicit assumption is that jurisdiction is exclusive, it isn't. Any country (or sub-national jurisdiction) that claims jurisdiction has jurisdiction, at least to the extent of testing that claim. Whether any given polity has jurisdiction depends on the particular law involved, some laws are only applicable within that countries borders others are extra-territorial, some are applicable to citizens but not non-citizens or vice-versa, etc.