In Mr. Medellin's case, the Mexican government is playing the part of a juvenile's parents - but in no way is the jurisdiction over the right to prosecute Mr. Medellin for his crimes affected. His case is essentially no different than that of an arrestee who wasn't read their Miranda rights, as far as I can tell, with procedural violations being at issue, rather than whether the United States has a right to arrest and prosecute Mr. Miranda in the first place.
On the contrary, in Medillin's petition, the Government of Mexico raises the issue of diplomatic protection of its citizens and has asked for an annulment of the conviction and sentence for Medillin. That certainly raises jurisdictional questions and materially affects the right of the State of Texas to prosecute Medillin for his crimes. See this quote from the brief filed on Medillin's behalf in the Supreme Court case:
Seeking relief on its own behalf and, in the exercise of its right of diplomatic protection, of its nationals, Mexico claimed that the United States had violated Article 36 in each of those cases and requested, among other relief, the annulment of the convictions and sentences of the 54 Mexican nationals