Drop caps in EPUB are a bit fussy. (Oddly enough, if you continue on to Kindle, they are dead simple and usually display exactly as intended.)
The only good way to control drop caps in EPUB is with CSS. It's not hard, but you want to apply a character style to the dropped letters, then make some tweaks to that style in CSS at export time. Here's the gist of it:
Use InDesign’s drop-cap style feature.
Create a “DropCap” character style and apply it to caps you want dropped. You may want to have it highlight the letter or otherwise announce its use, to keep layout management simple. (F'rex, make the letter red. You can change this in the CSS code.)
Now, in your own CSS code or in a copy of the generated style exported from ID, add !important to the font size change. That alone should make EPUB present the drop caps correctly, as based on the exported style, much as it does automatically in Kindle.
You can make other tweaks (such as changing the color back to blck), and may want to tweak the top-right-bottom margins to align the drop cap correctly in EPUB.
╟─ Word & InDesign to Kindle & EPUB: a Guide to Pro Results (Amazon) ─╢