Acquiring indices for anagrams of an input string
You're making an assumption that these strings contain just letters.  If there are spaces, digits, or letters with diacritics, then you'll end up with an ArrayIndexOutOfBoundsException.

isEqualCounts() is just a reimplementation of Arrays.equals(int[], int[]).  If you choose not to use Arrays.equals(), then I suggest starting with assert counts1.length == counts2.length;.

A more robust strategy, which doesn't rely on the assumption that the text is purely alphabetic, would be to check whether each sorted array of characters matches the sorted array of characters of the reference string.

You could optionally add a quick-but-crude check by calculating a "summary" or "fingerprint" of each string that consists of its length and, say, the sum of all its characters.  Any string whose fingerprint is different from the fingerprint of the reference could be immediately rejected.  The strings with matching fingerprints could then be checked more thoroughly.