What's your scientific source to claim that Cimmerian was Old Persian? It's not even widely believed that we have enough evidences to claim that Cimmerian was indeed Indo-Iranian, let alone Old Persian, which is a specific language of the Southwestern branch of the Iranic languages: Indo-Iranian > Proto-Iranic > Southwest Iranic > Old Persian. Cimmerian is actually thought by many to have been a sort of intermediary branch between Daco-Thracian and/or Illyrian (mostly the former, as far as I have read) and Indo-Iranian. There was probably such a thing as an "Albanized Iranian language", and in any case it is unlikely that Albanian had anything to do with Cimmerian in terms of recent linguistic origins. What probably happened is simply that the dialect continuum of the IE languages was not completely broken due to the expansion of just a few daughter languages up to the Iron Age, superseding most of the other "middle-ground" dialect groups (IE branches) that existed between them. There was probably a "Germanic-Celtic" language, a "Slavic-Indo-Iranian" language, a "Hellenic-Illyrian" language and so on, but those were not actual mixes of those IE branches, they were actually just dialects that shared features with one end and the other end of the IE dialect continuum. Cimmerian might've been one of the remnants of these extinct IE branches.
Analyzing the connections between two languages based on their supposedly sharing some phonological developments in common is very misleading (and that is assuming that those sound rules are exactly identical, and not just similar in their ultimate consequences - I'm not sure about that). Languages are much more than their phonology, no proper assessment can be done without considering above all the morphology and syntax (and, secondarily, the lexicon too)... in fact there are some sound changes that are pretty common throughout the world under the same or similar conditions, so that they may happen in almost identical ways in different languages, in different times and places, without necessarily one of them having influenced the other, or their having a recent common root. For instance a "satem-like" change happened in Old French, affecting even the /ka, ko, ku/ syllables (not just /ke/ and /ki/ as in most other Romance languages), but that doesn't mean that it must've had some influence from a satem lanuage. The sound changes were completely independent, it just happens that palatalizations and subsequent fricativizations or sibilantization of consonants are a very common development in many languages' evolution. E
ven if the sound change was identical and happened at the same time, that still does not imply necessarily an immediate common origin, because it may just point to areal features in a large Sprachbund, sharing some common linguistic trends.