You're still summoning them. The rings apply when you summon a soldier.
Not sure about that. They apply to Casting, not Summoning.
From the cards:
Commander’s Cape: ‘Once per round you may pay 1 less mana when you cast or reveal a command spell or cast a soldier creature spell’
General’s Signet Ring: ‘This mage may pay 1 less mana when he, or a Spawnpoint he controls, casts a soldier spell.’
Legionnaire: when summoned, you may pay 4 mana. If you do, immediately summon a Goblin Legionnaire from your spellbook, into the zone, as a free action.
(Compare the language on Legionnaire to the language on extending walls: "As you cast a wall, you may choose to pay an additional cost equal to the casting cost of the wall plus the wall’s Level. If you do, when the spell resolves, you may get a second copy of that same wall from your spellbook and place it as a continuation of the first wall." Nobody has ever taken damage from a Magebane for extending a wall, so that is certainly not considered 'casting'.)
I don’t think there is a correlation that ‘summon’=‘cast’, as you suggest.
From the supplement: ‘Summoning is the act of bringing a creature into play and placing it in the arena.’
Up to the release of the Academy Warlord there was only oneway to summon soldiers - casting either by the mage or a barracks. But now there seems to be a second option for these creatures.
So all the Legionnaires are Summoned, but only the first one is Cast and entitled to any discount.
The best cost I can see is the mage casting the first with both ring and cape: 1+4+4=9. From barracks only the ring applies to the first one, so 2+4+4=10.