Here are some free Esperanto books in the ePub format that you can use to test:
http://www.esperanto.be/fel/but/e-libro.php#senpaga
You'll see that the corpse of the books show the perfect diacritics on the ĉ, ĝ, ŭ because these books have embedded fonts. But you'll see also that the diacritics do not show in the table of contents. ADE doesn't use the embedded fonts for the TOCs, but it's own fonts. The only solution as far as I know: do not use ADE programs but use e.g. EPUBReader.