There is nothing wrong in making nafl `Umrah before or after `Umrah and Hajj (Tamattu`). However, to avoid any disagreement or confusion with regard to the intention, one can perform nafl `Umrah after finishing the rites of Hajj.
One can also perform it before Hajj while intending to perform Nafl `Umrah. Then when you want to make the `Umrah of tamattu`, it should be with a new intention of tamattu` after removing the Ihram attire of the first `Umrah. Then you have to wear Ihram for the `Umrah of tamattu`.
Allah Almighty knows best.