“USAGE It is sometimes held that none can take only a singular verb, never a plural verb: : none of them is coming tonight, rather than : none of them are coming tonight. There is little justification, historical or grammatical, for this view. None is descended from Old English nān, meaning ‘not one,’ and has been used for around a thousand years with both a singular and a plural verb, depending on the context and the emphasis needed.”
You’re right though that it’s weird to mix both singular and plural verbs for the same subject.
“USAGE It is sometimes held that none can take only a singular verb, never a plural verb: : none of them is coming tonight, rather than : none of them are coming tonight. There is little justification, historical or grammatical, for this view. None is descended from Old English nān, meaning ‘not one,’ and has been used for around a thousand years with both a singular and a plural verb, depending on the context and the emphasis needed.”
You’re right though that it’s weird to mix both singular and plural verbs for the same subject.