Data Fields always associate with a Page other than Contacts. So, start on a page other than Contacts to select the Recipients to send to. The Contact ID Field on the Page's record determines the Recipients.

For example, you want to use Data Fields from the Opportunities page. When you select the Opportunities and launch the New Message Tool, then the recipients are the Primary Contacts of each Opportunity. This is specified in the Contact ID field in the specified Page:

If needed, you can add or change the value (SQL string) as long as it ends in "Contact_ID". This way, you can attach the Contacts associated with the selected records to the Messages.