There are actually two issues concerning this topic: May i have everyone's attention,. There is a comprehensive article on the topic on grammar girl:
Your deduction, that not everybody's cup of tea means not to everyone's liking, is absolutely correct. In my experience, the spelling checkers get confused by contractions. Should it be everyone's, everyones' or everyones?
In fact, to catch someone's eye is an idiom, not eyes. the question is not about everyone being singular or plural. The indefinite pronoun 'everyone' is a singular pronoun. Are the words everyone and everybody singular or plural? Joe got everyone's attention and started to speak.
An example would be it flew over everyone's heads, or it flew over everyone's head. What would be correct in this case and why? Would the noun following everyone's be plural? The expression commonly used in both the affirmative and negative.
Everyone who is coming will receive a gift. The possessive form is everyone's (the form everyones' is incorrect).example: The possessive of everyone is everyone's, in the same way the possessive of everybody is everybody's. Unless of course you’re a buddhist or a cat, in which case everyone has multiple lives and both would be correct, depending on context.