... I am wondering do I need to reinstall clean my Mac to uninstall it?
Yes. Using its uninstaller module will remove the folders that remained in your Application Support folder, but their presence is not the reason for the popups. The fact those folders are still there was merely an indication that CMM was not uninstalled properly, and that other system-altering components probably remained also.
You have to choose CMM's "complete uninstallation" option to completely remove CMM. As a minor point, that option will leave a CMM folder buried deep within your Photos Library, but only if you are using Sierra's new Photos app.
How do I make sure I only transfer over my iTunes musics, photos library and documents from my back up? Keeping everything else like a new mac?
That's even easier. Completely erasing your Mac, and then using "Enter Time Machine" to restore your iTunes folder, your iPhoto Library, and your user Documents folder will migrate only those items, respectively. It is impossible for anything else to be migrated including whatever process might have been causing the popups. If you do that then there is no need to reinstall CMM only to uninstall it properly.
If the popup nags return, it's due to another cause that requires further investigation.