When you switch from whatever to Japanese, the toolbar should look like this:
<img src="http://airelle.info/toolbar_jp1.png">

Click on the "A" (to the right), and select hiragana, it should look like this (maybe with the little keyboard icon too):
<img src="http://airelle.info/toolbar_jp2.png">

Once you have that, you type japanese by typing the syllabs, eg, typing "k a" will input か, typing "nihongo" then pressing space will input　日本語.