That's what I thought - is that always the rule, the extra accent on the last syllable before the pronoun if the main accent is on the ante-penult? Or are there exceptions?
I believe the rule is to always put an accent on the last syllable before an unaccented clitic (which in Modern Greek is, I think, just the possessives) if the accent is on the antepenultimate.
Note, however, that in Modern Greek it's not always clear from the spelling how many syllables a word has, as the letters that spell the sound /i/ can also spell the sound /j/ -- one of them is a vowel and contributes a syllable, the other is a glide or semivowel and does not make an extra syllable.
So e.g. άδεια can be either two syllables "ά-δεια" (empty) or three "ά-δει-α" (permission, leave), and only the second case would need an extra accent when followed by a clitic.
At this app this rule is always neglected. I think this is a mistake of the developers