From H. W. Smyth, Greek Grammar, I §§149-188
GENERAL PRINCIPLES, ANASTROPHE, CHANGE OF ACCENT IN DECLENSION, INFLECTION AND COMPOSITION, PROCLITICS, ENCLITICS
Cf. Long and Short duration of Greek vowels (at KOINONIA Greek Forum)
169. Final -αι and -οι are regarded as short: μοῦσαι, βούλομαι, πρόπαλαι, ἄνθρωποι. But in the optative -αι and -οι are long (λύ̄σαι, βουλεύοι), as in contracted syllables. So also in the locative οἴκοι at home (but οἶκοι houses).
a. The difference in the quantitative treatment of -αι and -οι depends on an original difference of accentuation that may have vanished in Greek. -αι and -οι, when short, were pronounced with a clipped, or simple, tone; when long, with a drawled, or compound, tone.
170. The quantity of α, ι, υ may often be learned from the accent. Thus, in θάλαττα, ἥμισυς, πῆχυς, δύναμις, μῆνις, the vowel of the last syllable must be short; in φίλος the ι must be short (otherwise φῖλος).
171. Contraction. – If either of the syllables to be contracted had an accent, the contracted syllable has an accent. Thus:
a. A contracted antepenult has the acute: φιλεόμενος = φιλούμενος.
b. A contracted penult has the circumflex when the ultima is short; the acute, when the ultima is long: φιλέουσι = φιλοῦσι, φιλεόντων = φιλούντων.
c. A contracted ultima has the acute when the uncontracted form was oxytone: ἑσταώς = ἑστώς; otherwise, the circumflex: φιλέω φιλῶ.
N. 1. – A contracted syllable has the circumflex only when, in the uncontracted form, an acute was followed by the (unwritten) grave. Thus, Περικλέὴς = Περικλῆς, τῑμάὼ τῑμῶ. In all other cases we have the acute: φιλὲόντων = φιλούντων, βεβὰώς = βεβώς.
N. 2. – Exceptions to 171 are often due to the analogy of other forms.
Reference address : https://www.ellopos.net/elpenor/lessons/greek-accentuation.asp?pg=5