When using Migration Assistant, if your old Mac has an account that has the same name as an account already on your new Mac, you'll be prompted to either rename the old account or replace the one on your new Mac. If you choose to rename, the old account will appear as a separate user on your new Mac with a separate home folder and login. If you choose to replace, the old account will delete and then replace the account on your new Mac, including everything in its home folder.
From what you say above, if the files from your old Mac are not in the accounts on the new Mac, then it would seem that nothing was migrated.