Re-posting from a direct apisupport contact.
The UPSleep object you get by using the iOS SDK always has a value of 0 for the totalDeepSleep parameter. Using the official UP app i’ve verified that this is not the case.
Currently, the UP API sleep endpoint reports deep sleep as "sound" sleep, and thus, the iOS SDK will report deep sleep as sound sleep.
In the UPSleep object, the parameter you want to look at is called totalTimeSound.
For more details on the underlying issue with the sleep endpoint, please see my answer to this question: How can I get deep and REM sleep data from the Jawbone UP API?