Azure and Verdant dusts have been "deprecated" and are being phased out. They will not exist in the Minecraft 1.9.4 version of the mod.
The Calcinator has been changed now so that it will only produce either Ash or Minium Dust. What you get is the result of a probability defined by the EMC of the item you are calcining and the EMC value of Minium Dust.
So for example, let's say you are calcining a piece of cobblestone and that the EMC value of Minium Dust is 8,192 (the default). There you have a 1 in 8192 chance that that piece of cobblestone will calcine into a single Minium Dust. However if you calcine a diamond (default EMC value of 8192) you will have a 1 in 1 chance, and you will get a single Minium Dust as your result.
Let's say however you attempt to calcine something that has an EMC value larger than a single Minium Dust. Let's say that, I don't know, Iridium has an EMC value of 10,000. What you will find is that you will always get at least 1 Minium Dust, with a chance to get 2 Minium Dust. The reason for this is that the function sees that you have more EMC than a single piece of dust, so it subtracts that and notes that you should get at least one. Then it looks at the remaining value (1,808) and tries that probability (~22% chance of getting a second Minium Dust).
Hopefully that clears things up for everyone regarding the new Calcinator mechanic