Member content and CDN are not compatible.
The cache control headers are the same between a public content and a member content when you defines the cache control value into the configuration file.
"caching": {
"contentAPI": {
"maxAge": 86400
},
"frontend": {
"maxAge": 86400
}
},
The solution could be : if the content is a member content, return a private control cache to avoid the content to be cached into the CDN.