I don't know off-hand of any textual accounts of translators (there may be in e.g. Ctesias, but I don't know off the top of my head) but apart from the undoubted use of those, there was also a lingua franca since Neo-Assyrian times: Aramaic. Though the court languages of the Achaemenids were Persian, Elamite (also the administrative language of Persia proper) and Akkadian, it is clear that Aramaic was very widely used - Aramaic script formed the basis for both Parthian script and Sanskrit alphabets; Arabic has numerous loanwords from Aramaic; it outcompeted Hebrew as a common tongue in Judaea (hence why many know it as "the language of Jesus").

In the case of inscriptions, they are commonly bi- or trilingual; two famous examples are the Rosetta stone (Demotic, Hieroglyphs, Greek) and the Behistun inscription (Old Persian, Akkadian, Elamite). Certainly an important treaty would be in either a lingua franca or in the native tongues of both parties.

Alexander's conquests led to the proliferation of what we call Koiné Greek, of course, and it was pervasive enough in the East that still in Sasanian times (3rd c AD) we have parallel inscriptions in Persian, Parthian and Greek. It may be useful to keep in mind that when moving from town to town, at some point you end up at a language frontier, but within that frontier you're going to have an easy time finding bilingual people. Moving through sufficiently urbanized areas, finding translators is unlikely to be a huge issue.

Finally: court languages differing from majority languages are very common throughout history, especially when you account for how much regional dialects varied and how different prestige language could be from common language.

I hope that cleared some things up for you?