The German examples on that wiki-page actually show what an apposition is and what not (I'm talking about the sample sentences, not the badly-written article). In the sentence "Tantalus, in die Hölle geschickt, erlitt Strafen.", you have an apposition indeed because the participle comes as an after-thought to Tantalus and has to be pronounced with a slight speech pause in the places where the commata are. However, while this might be theoretically possible, it's rather unnatural German -- the kind of German you usually only find in the Latin translation attempts of students who are overwhelmed with the task of properly rendering a Latin sentence in regular German word order. I remember that my Greek teacher actually hated those constructions to the core.
The more natural translation would be to use a participle construction in German as well, which would require a change in word order: "In die Hölle geschickt erlitt Tantalus Strafen." -- That would be the regular German sentence, and here, the participle construction is not and cannot be an apposition because it does not even stand appositive to the noun (it is set off by the verb).
Likewise, while in textbook Latin a participium coniunctum often follows a noun directly and could in such a position theoretically be pronounced like an apposition, it can in reality actually stand anywhere in the sentence - mainly due to the fact that it is not an apposition. So, instead of "Tantalus ad Tartara missus poenas dedit" I could also construct this sentence as "Tantalus poenas dedit ad Tartara missus"