The contraction of is is 's. It attaches to the word before it and takes that word's final sound: /z/ after voiced endings, he's /hiːz/; /s/ after voiceless ones, it's /ɪts/.
He's here. The contraction sounds as /z/ after the voiced ending of he, matching the standalone word is /ɪz/, whose spelled S is voiced.
That's true. After the voiceless /t/ of that, the contraction shifts to /s/ /ðæts/, but it still expands to That is true.
The standalone word is is always /ɪz/ with a voiced /z/. In the contraction, the sound follows the preceding word instead: it's /ɪts/ takes the voiceless /s/, while she's /ʃiːz/ keeps the voiced /z/.
Restriction: 's never stands alone. It must attach to the word before it, so a short answer uses the full form: Yes, he is /hiː ɪz/, never a bare 's.
Watch the phonetic trap: the S in is is printed as a voiceless-looking letter but sounds as /z/. So is is /ɪz/, and after voiced endings the contraction keeps that voicing: he's /hiːz/, there's /ðeəz/.
After voiceless sounds it devoices to /s/: that's /ðæts/, it's /ɪts/. Same spelling, different IPA sound, decided entirely by the final sound of the word before it.