The rule should not mark it unread. My test rule did not. You may want to try deleting the rule, then adding it again in iCloud.com.
However: secondary folders do not get push notifications. When I send an email that has a Cloud rule, it gets moved before it goes to the Inbox (so it seems). This means that Mail does not receive a push notification. Until I actually open the folder in question Mail does not look at the server for that folder's contents; so it does not know there is an unread email in the folder.
Once I navigate to the folder the new mail is loaded, and shows up as unread. You must have email already in the folder, otherwise the new email (being the only one there) will automatically be opened and marked as read.
My Gmail Exchange account can be set up to push selected folder, but I can't not find a comparable setting for iCloud. I do not see any solution to your problem.