Did that really provide any phonetic guidance? All it appears to say is that it is just like "cingulata" except the "c" should be pronounced "tch".

As you note "cingulata" is fairly uncommon. I have no idea how to pronounce that, and so their guidance still leaves me in the dark about everything but the first letter.

For phonetic guidance something using the International Phonetic Alphabet seems like the way to go. I think that would give something like this: tʃiŋgyəˈlātə, -ätə

That's just a guess taking the IPA for cingulata from Merrian-Webster (siŋgyəˈlātə, -ätə) and replacing the "s" with the "tʃ" that the Macmillan dictionary gives for the "tch" in "latch", which is the first word that came to mind that has a "tch".

(Also, I believe many publications use their own variants on the IPA, so I'm not sure that what I gave is actually proper. If MW and/or Macmillian have their own, the above could be some weird bastardization with little meaning).