I have found that when a spear from Kalista is in a minion and you try to last hit the minion with relic shield it simply gets rid of the minion. Doesn't give you the gold, the health, or the credit for the minion kill. Just simply gets rid of the minion. I don't know about how it works with the upgrades from Relic shield but I know its for sure on normal Relic Shield.
This just happened to me, I was Leona and only had Relic Shield first item too.
I found that it probably has to do with the Soul-mark passive of the Soul-mate buff. Seemingly the **damage **bonus from hitting the same target does not "belong" to the support (or kalista?) and thus Relic Shield does not trigger when this damage is the cause of a minions death. On the contrary, a solution to this is to proc Soul-Mark before executing the minions, basically hitting a minion twice (make sure you hit early enough), exploiting the cooldown of this effect to get the minion gold.
