I try to save some time by only doing writing and reading prompts. The latter I prefer to do on the website, and when I do so, everything works as expected, almost. And as a bonus Skritter tracks my tone progress, without me ever seeing the tone prompts - which is great.
However, I think I have found there to be a problem with this approach:
Ever since I disabled tone prompts, new reading prompts have tended to appear as "new" twice, if I study on the iOS app. That is to say, I study it the reading prompts on the web app, and later I will see the same reading prompts on iOS, marked as "new." (I have not noticed this problem on the web app, that may just be a coincidence, though).

I have just gone and checked to make sure, and indeed, I should only receive writing and reading, but still, I see in my words that a tone prompt is due in eleven hours:
https://dl.dropboxusercontent.com/u/1309600/Screen%20shot%202013-05-01%20at%206.35.59%20PM.png

Edit:
For some reason the link redirects to:
https://dl.dropboxusercontent.com/u/1309600/Screen%2520shot%25202013-05-01%2520at%25206.35.59%2520PM.png
Try copy-pasting the adress instead...

Edit 2:
OK, so it does also affect the web app:
https://dl.dropboxusercontent.com/u/1309600/Lu1.png
https://dl.dropboxusercontent.com/u/1309600/Lu2.png

What is up with the links? %20 changes to %2520.

Hove over the "New Word" when you see it. Does it say "New tone?" The tone prompts aren't done as part of the reading prompts on the iOS app where you're seeing them first, whereas on the web app I think what's happening is that the tones are what's triggering the "New Word".

I just studied 泰, 避讳, 辩, 奉, 韦... and yes, they all showed "Holy smokes, a new word! (At least, the tone is new.)"