Whelp, that Dutchman is wrong. (reference)
To elaborate a bit more: the singular is "idee", with a long vowel. The trema (two dots) on a vowel means that this vowel is in a separate syllable from the vowel before it. So in "ideeën" it comes on the last e, to make it clear that the word should be pronounced "i-dee-en" (ee-day-un) and not "i-de-een" (ee-duh-ayn).