I think I found something. Rule of Specialty.
Additionally, most extradition treaties contain a provision known as the "rule of specialty." This rule provides that a person who has been extradited may be prosecuted only for the offense listed in the extradition request. The rule is to ensure that a person is not extradited on a pretext, only to be prosecuted for an offense for which extradition may not be allowed. The rule of specialty may be waived by the nation¹ from which a person is extradited.
This is a little bit different in that the secondary prosecution would be handled by a different jurisdiction (US) versus the primary jurisdiction (Sweden). However this doctrine of the Rule of Specialty increase the chances that Ecuador is within its rights in demanding assurances that Assange will only be prosecuted for what is alleged in the extradition request. The Rule of Specialty seems to be very similar to what Ecuador is demanding.
¹ Now the nation is Ecuador since Assange is under their jurisdiction. Ecuador is not allowing the Wikileaks publishing prosecution on the grounds that it is a politically motivated prosecution.