'Yemls Phonemes

A question:

'Yemls has 4 vowels, distinguished for low vs. high and front vs. back, and
12 consonants. The syllabary is laid out with a column for each vowel and a
row for each consonant with an additional row for the null consonant.
Currently, each vowel and consonant is described as a phoneme. However, in
actual pronunciation a couple things occur. One is that how some of the
consonants are pronounced depends on whether the vowel is front or back,
e.g. /s/ is [s] before /u/ and /o/, but is [S] before /i/ and /e/. Another
is that /u/ and /i/ are eliminated under certain conditions, so that the
possibility of minimal pairs occurs distinguished only by [s] vs. [S].
If I understand correctly, that means that these should be reanalyzed as
separate phonemes (instead of both being /s/). Is that correct?

Jeff