You should have Migrated from the Time Machine backup. That's the easiest way.
You can still do so, but if you set up the new Mac with the same username as the old one, it may be more difficult.
To Migrate the old data, open Migration Assistant from the Utilities folder and follow the prompts.
You can also Option-click the Time Machine icon and choose "Browse Other Backup Disks" and restore files that way.