If you look at the groups - you may find one of more groups listed as All on My Phone or associated with and email not you iCloud ID. You need under settings mail contacts, calendar near the bottom to set the default account for you contacts to be the one that is associated with your iCloud. Otherwise new contacts will not be placed in the iCloud world.
No I don't know of a good easy way to move those that aren't associated to the associated group of contacts.