The grammar is wonky on that codex entry. Covering the summoning of spirits doesn't mean that spirit magic allows them to summon spirits or even that spirits can be summoned. Alchemy covered the conversion of lead into good but it wasn't a possible thing to do.
In "Asunder", Rhys is able to summon a weak spirit to scout for him, no blood involved. EDIT: It was clueless enough to think that suits of armor were actually templars, which kinda messed with the scouting bit. I thought it was cute.
That's how I figured the "animate dead" spell worked in DA:O: Summon a weak spirit into a vacated skinvelope and it mostly follows your orders by virtue of not really being developed enough to have any sort of long-term goal.
My idea for a true specialization was to have you interact with a single spirit, continually summoning the same one to animate the corpses you choose to animate. As you expand in the school, you can influence how the spirit develops, which would influence your abilities. Hunger demon results in devouring corpses, Sloth demon results in shambling corpses, etc. Eventually culminating in the ability to have it animate a group of corpses into a Harvester.
Obviously not how this is going to work, but there you have it.