Normally high vowels (i and u) can be devoiced between two consonants that are also voiceless, or between a voiceless consonant and the end of a word. Since 's' is voiceless, SHI can become devoiced (if it's followed by another voiceless consonant or the end of the word). When we say JI is constructed from SHI, we mean it's the voiced-consonant version of JI. Since the consonant is voiced, typically the following vowel is also voiced.
Non-high vowels (a, e, and o) can also be devoiced, but this is a lot less common.
It can depend on other things too, like register (formal and feminine registers tend to voice the vowels more), dialect (devoicing occurs a lot more in the Tokyo dialect than it does in Western dialects) and how common the word in question is (more commonly used words are more prone to devoicing). For instance, I've heard shikashi ("however") pronounced with both 'i's voiced, with both unvoiced, and with the first one unvoiced and the second one voiced.
Note that when I say a voiceless consonant, I mean an obstruent like 't/ch', 's/sh', 'k', and maybe 'h'. Sonorants like 'm', 'n', and 'r' are technically voiced, even though they aren't marked by a dakuten in the kana (but they also can't have a dakuten added, because they're already voiced). Also 'w' is voiced and 'p' is unvoiced (even though it does have a handakuten in the kana), but in native Japanese (i.e. excluding loanwords), 'w' is never followed by a high vowel, and I think 'p' is only followed by a high vowel in onomatopoeia, so this is really a consideration for how they affect the preceding vowel.
Last edited by thegooseking on September 19th, 2017 1:08 pm, edited 2 times in total.