The interpretation of Hittite /ts/ is still somewhat of an open question.
First, Hittite cuneiform could have distinguished voiced and voiceless stops in many positions…but it didn't. For example, the signs ta and da are used pretty much interchangeably, even though Sumerian and Akkadian uses them consistently to indicate a voicing difference. However, Hittite scribes were consistent (in a way Akkadian and Sumerian scribes never were) in distinguishing between at-ta and a-ta—that is, single vs double consonants.
This is the distinction that Kloekhorst transcribes as /t/ vs /d/, but only for the sake of easier typography: he doesn't claim there was actually a voicing distinction there. It was almost certainly some sort of length instead.
Now, was there a consistently-written difference between az-za and a-za? That's less clear. It certainly wasn't as consistent as at-ta vs a-ta, so it's still debated whether there was a difference between short and long /ts/—or whether length mattered in clusters at all! There are ways that length could have been indicated in consonant clusters, like writing ar-at-ta vs ar-ta (VC-VC sequences were avoided except when writing clusters), but these methods don't seem to have been used.
So whether there was any difference between /dst/ and /dzd/ and /tst/ is an open question. If there was, it certainly wasn't indicated in the writing. Kloekhorst uses this transcription because the root was /ed/ (or maybe /ʔed/). But it's very likely that the difference between /d/ and /t/ was neutralized in this position, and the choice of which transcription to use is a matter of style more than anything measurable.
