There is no clear answer to the title question in general; it may depend on the sounds, or the language. (Well, unless you define "assimilation" in such a way as to explicitly refer to a process that changes one phoneme to another.)
Examples like these are part of the reason why people have come up with concepts like "archiphonemes" (although I have the impression that the archiphoneme concept isn't used much in current theories of phonology).
English "cats" and "missed" are usually transcribed with /s/ and /t/
Within frameworks that use the concept of "phoneme", the most common analysis that I have seen treats English plural [s] and plural [z] as different phonemes, /s/ and /z/. These could be analyzed as both corresponding to underlying "z", but that underlying "z" would be changed into the phoneme /s/ in a word like cats. (I used quotation marks around "z" because I'm not sure what kind of phonological entity it would be treated as.)
One reason for supposing that the [t] in words like "missed" is the phoneme /t/ is that there is no audible contrast with a word like mist. And mist is typically analyzed as ending with /t/ rather than /d/ (there are various reasons for this, among them native speaker intuition, spelling, and etymology).
There are non-standard variant spellings of the "-ed" and "-(e)s" suffixes that provide limited support for either analysis; e.g. "gript" as a variant spelling of "gripped" vs. "Flipz" and "Bratz" as brand names.
Transcriptions of languages with "final obstruent devoicing" often use the symbols for voiced consonant phonemes
The situation in languages with systematic "final obstruent devoicing" like Dutch, German, or Slavic languages may be a bit different. There is a body of research suggesting that the contextual neutralization of voiced and voiceless obstruents in some of these languages may be "incomplete" at the phonetic level: even though the sounds are close enough that a listener cannot reliably distinguish voiced phonemes from unvoiced ones, apparently speakers may produce slight differences on average between words with underlying voiced and voiceless sounds. For German, the differences are supposed to show up in the duration of the vowel in the syllable ending in the "devoiced" consonant. Here is an article about the alleged phenomenon of "incomplete neutralization" in German: "The Nature of Incomplete Neutralization
in German: Implications for Laboratory
Phonology", by Bodo Winter and Timo Röttger, 2011. However, they "argue that IN can be explained even without recourse to the phoneme, making almost no theoretical assumptions" (p. 63), so you'd probably have to look at other literature for detailed accounts of how to reconcile this kind of data with theories that deal with phonemes.
Although I mentioned German together with Slavic languages, there are actually notable differences in their treatment of voicing. German, like English, has a so-called "fortis-lenis" contrast where phonologically voiceless/fortis plosives are aspirated at the start of a syllable, and phonologically lenis/voiced plosives are unaspirated and "weakly" voiced (or not phonetically voiced at all). There is no regressive assimilation from voiced obstruents to preceding voiceless ones.
In contrast, Slavic languages (also Dutch, if I remember correctly), contrast tenuis voiced stops with fully voiced stops, and do show regressive assimilation of voicedness. I don't remember seeing literature about any possible "incomplete neutralization" effects in the context of regressive assimilation to voicedness, but I haven't tried to look for it yet. One argument for treating this assimilation as phonetic rather than phonemic would be that there are some circumstances where it would create otherwise-unattested phonemes: for example, Russian phonology is typically analyzed as containing a phoneme /t͡s/ but not a phoneme /d͡z/, and regressive assimilation can create [d͡z].
Here is a thesis that I found (I only skimmed it) that transcribes "devoiced" obstruents in Russian using the symbols for voiced phonemes: Voicing and voice assimilation in Russian stops, by Vladimir Kulikov, 2012.
