Yes, I am a finalist of national geography olympiad too and I can tell you that Cyprus belongs geographically to Asia. Georgia, Azerbeijan and Armenia too.
Each federation chooses where they want to play. Israel was a political choice; In football years ago, they were assigned to the Oceania group in World Cup qualifying until they became full members of the European federation UEFA. They were originally assigned to Africa with the other middle eastern coutries which often led to walk/overs or withdrawals (because politics). Sometimes, it's for the level of competition: the Australia football moved from the weaker Oceania (OFC) to the stronger Asia (AFC).