I can understand being able to charge your own citizens for crimes committed overseas (Australia does that). But I cannot see how a country can have authority over another countries citizens that commit crimes overseas without the other country giving it to them. Isn't that a direct attack on another countries self rule?

It creates a stupid set of rules. Where you can do something that is legitmate in your country but if a Spaniard is involved you might be commiting a crime that you have no idea about.