Why do you believe that the tribunals lack evidentiary standards (cite?)? Recall that the vast majority of the world community does not adhere to a Common Law system, but rather relies on the judge-made law of the Civil Law system. Many would sugest that the tribunals actually have a larger body of law to draw upon (conceiveably anything in International Law), and would therefore be more likely to come to a just outcome that the ICC which (if bound by rules of stare decisis, as you suggest below) would have a much more limited body of decisions from which to draw its reasoning.
Finally, tribunals are not perceived by many as being conceived ex nihilio (or, "out of nothing" for those new to latin...lol), but rather, out of the context of a more traditional international prosecution. While the ICC may be very "comfortable" to americans, as it contains some of the aspects of our legal system (as described above), we must remain aware that in the context of international prosecution (or International Law in the larger sense...), this is a very new concept/institution.
The evidentiary standards of the ICC are much more delineated and specified to preset definitions and standards than in the trials of the ICJ where cases do not allude to former case law as one would expect in a civil system, you are quite right. However, the ICC does adhere to a specific format regarding admissibility in adhering to stages of proceedings as noted below which is not present in the ICJ procedings. Such procedings bespeaks to my mind a more than coincidental correlation to federal standards of evidence as I have purviewed them on Lexis..In chapter 4,section 1,rules 63-75 below alluded to are rules enunciated as principles not present in the ICJ lexicon, to be sure.This earmarks more than a civil system, but a hybrid composed of the elements of common law rulings on evidence which have been codified in anglo american law and stare decisis,but codified from their ulings in specific court cases and statutes.Note the underlined sectons below regarding admissibility,inspection and disclosure. The similarity of standards ,though encased in a civil type of system. are resonated in our discovery and evidentiary standards in our common law,but established by ruies of the court and by the Rome statute.Note epecially rule 73 regarding priveleged communications. These rules were stated not capriciously, but with the intent of focus not heretofore made in the canons of international law as applied to the specific crimes over which the ICC has jurisdiction.They have taken common law standards more in focus and enabled statutes in a civil frame of reference.The need for this was made manifest in the Rome statute dealing with thee unique crimes.The larger body of law to draw upon has not been done in the modus opeerandi of stare decisis as has occured in U.S. Supreme Court decisions , and that is what I indicated by the term "ex nihilo" insofar a a clear citing of allusions has not occured as in our Supreme Court cases explaining the holdings of cases specifically. The ad hoc manner contains a lack of such explication, though exegesis is done differently in the civil asystem. The borrowings are evident and hybrided into a statute arrangement in the civil mode, I believe.The larger body of law has not been sytematized to fit the specific crimes under which the ICC has suzerainty nor codified into specific digests of compilation as has occured in our law.The limited body of law to draw on by the ICC would not be applicable as the ICC could still draw on the resources of the ICJ through their cooperative agreements whch was why those agreements were made iniotially but applied to a recodified civil system of the Rome statute and the rules of the ICC.