"Ocurrido" there is optional. Its value is adjectival.
(Note: I find a mistake in the Spanish translation -- if the interlocutor is referred to as "Mr. Warren" (señor Warren), he should be formally treated as "usted", not informally as "tú"):
- Le pedí que viniera, señor Warren, para que no malinterprete el incidente (ocurrido) con el señor Tolly.
The participle phrase is an abridged relative clause:
- Le pedí que viniera, señor Warren, para que no malinterprete el incidente que ha ocurrido/que ocurrió con el señor Tolly (I asked you to come, Mr. Warren, so that you do not misinterpret the incident which has occurred/which occurred with Mr. Tolly.)
The closest "ocurrido" seems to get to English is the rather awkward phrase "having occurred" (contrary to what I thought, "occurred" alone is even much less usual):
- I asked you to come, Mr. Warren, so that you do not misinterpret the incident having occurred with Mr. Tolly.
After doing some research, I have found here grammatical evidence that, unlike in English, abridged relative clauses using a past participle can be formed not only with transitive but also with some intransitive verbs in Spanish. In English a passive meaning will always be required for the past participle to be used in an abridged relative clause:
- The incident (that was) caused with Mr. Tolly was misinterpreted.
- El incidente (que fue) causado con el Sr. Tolly fue malinterpretado.
However, in Spanish we can come across some abridged relatives using intransitive verbs (these examples are taken from or based on verbs used in the mentioned source):
- La niña [nacida en el hospital] fue dada de alta al día siguiente. (The girl (who was) born in hospital was discharged the following day) (While "nacer" is intransitive in Spanish, it has a transitive origin in English: be given birth).
This other example is not so clearly one of an intransitive verb, because "ser muerto" can be interpreted as the passive form "be killed":
- El piloto [muerto en aquella batalla] fue enterrado junto a sus compañeros. (The pilot (who was/got) killed in that battle was buried with his partners)
Of all the examples contained in the source, another that illustrates the difference between English and Spanish is "llegar":
- Noticias llegadas de Alemania informan que España ha ganado la Eurocopa. (News from Germany report that Spain has won the Eurocup) (As is the case with "incident occurred", I also find examples of "news arrived" in this abridged relative pattern on the Internet, but I doubt how idiomatic they may be)
Others are "venir" and "salir" (in English a different transitive verb will be used). Notice that the gender/number variation accounts for the adjectival value mentioned at the beginning:
A V-ing form will be used to refer to a current or future situation:
- The products coming out soon are ...