I am still confused how to follow the singular pronoun "each" by the plural possessive pronoun "their".
Not only these examples I state here, but every day I notice such examples everywhere; in books of Google as well as in many pages, for example, Cambridge.
Here are from Yourdictionary:
Italy’s and France’s economies are improving. (Each country possesses their own economy)
Mark’s and Susan’s dogs don’t get along together. (Each person owns their own dog)
And here is another example from Cambridge :
Each member of the community should take pride in their local environment.