Your deduction, that not everybody's cup of tea means not to everyone's liking, is absolutely correct. I have the following sentence: In fact, to catch someone's eye is an idiom, not eyes. the question is not about everyone being singular or plural.
The possessive form is everyone's (the form everyones' is incorrect).example: Would the noun following everyone's be plural? The indefinite pronoun 'everyone' is a singular pronoun that takes a singular verb.examples:
May i have everyone's attention,. Are the words everyone and everybody singular or plural? In my experience, the spelling checkers get confused by contractions. Should it be everyone's, everyones' or everyones?
The expression commonly used in both the affirmative and negative. The possessive of everyone is everyone's, in the same way the possessive of everybody is everybody's. The indefinite pronoun 'everyone' is a singular pronoun. There is a comprehensive article on the topic on grammar girl:
What would be correct in this case and why? 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. Joe got everyone's attention and started to speak. There are actually two issues concerning this topic: