Its a bit more complicated than that.
The Centurion and Barbarian used to be regular features on the global map, then they discontinued them, and people complained about it,as you could only then get their materials from Uber invaders,or by purchasing coffers,for clan points in the store.(you still can )
I do not know when the clan store coffers where first added.
Fairly recently,both of these two "extinct" invaders made a return to the global map, however they do not remain as long as the rest of them do, and apart from one occasion thus far, only appear for 24 hrs.
It looks like you can get the equipment from the Avarin invader.
So attack Centurion Invaders when they are on the map; yield Gift of the Gods tiles; and attack Avarin Invaders (if you have enough energy and, in that case, drops can be from other invaders not exclusively Centurion).
You can also use Loyalty points to buy Centurion materials in the Clan Store - but you have a better use for Loyalty Points. Or you can use gold to buy coffers of materials in Items - Treasure but it is random chance what materials you get and you have better uses for gold.