It's not really beast taming though. Taming would imply that they are initially wild or feral, and through your actions, become domesticated. Which, in a convoluted sense, may be technically true. But, the term beast taming doesn't really adequately describe the skill.

Summoning is more like conjuring, resurrecting, or even necromancy. You're taking inanimate objects, often dead animal parts, and imbuing them with magic (not the skill magic, but in the colloquial sense) so that they may be used to summon the spirit of the dead animal.

The way I understand it is that the spirit is contained within the charm. Similar to how a soul is contained in a soul gem in Skyrim, for example. This happens when you kill a creature (through combat or hunter) and it drops a charm. This charm is then combined with the tertiary ingredients, and shards (which are shards of the spirit plane obelisk) to create the pouch.