It seems that it can not be helped depending on the application. Let's use the "down key".
You can not select a suggestion on Mac OS X by pressing the TAB key.
Some Mac OS X applications may not have the ability to select a suggestion from the TAB key. This is a problem caused by a conflict between the shortcut assigned by the application to the TAB key and the key assigned by Google Japanese input to the suggestion. Use the cursor down key to select the suggestion. Note that iTunes and Adium are currently known to fall under this issue.
- Google Japanese input 2.17
- Mac OS El Capitan 10.11.4