The lazy answer is, things work differently on Coldharbor than anywhere else since it is not part of the Plane of Tamriel.

However I think it is the voluntary nature of the Hist Sap donation that keeps the spirits calm, vs. the violent crime of the Dominion in stealing it. Or it could be the vampiric shard is masking the process.

This is true. As a lover of Argonian lore, I'll try to explain. The sap does hold the memories and souls of the Argonian people. Think of it as the Navi and the Sacred Trees in James Cameron's AVATAR. An Argonian is basically soulless until they lick the sap of a Hist. The body is just a shell to hold the soul. By licking the sap, it transfers a soul to the Argonian child. This creates a link between the Hist and Argonian. The Hist literally becomes a part of the Argonian. This makes it so the Argonian can hear, or at least feel the Hist's presence. Should an Argonian die, his/her soul returns to the Hist that they licked from as a child, along with their memories. But if you burn the sap, you're killing billions of Argonian souls, destroying their history, and everything. The Hist determines what soul the child gets and can add memories, if it so wishes. You could get the soul, small bits of memories, and skills of your ancestor. So Argonians believe in reincarnation.

There's a quest in the EP where the AD was using Hist sap to create Skin Stealers. This sap was tainted and there was so much of it, that the Hist that produced it was likely dead. Meaning the souls in this sap were likely lost, and if not, it'd of taken hundreds of years to repair the damage. So burning it was the best available option at the time, but hardest choice an Argonian could ever make.

As for the Hist in Coldharbour, it's similar to the Hist in 'Shadows of the Hist' dlc. It was psychotic. It made the Argonians ignore the screams, making them believe everything was ok. It thought that by sacrificing billions of lives would save itself, or the Argonians. Instead it was killing itself, and once dead, the souls of the Argonians connected to it would also be lost. Left to wonder until a new Hist takes them, but they're in Coldharbour. So their souls would be trapped for eternity. A Hist's sap is basically its blood, as the Hist aren't really trees as said by an Argonian female, in Stormhold, to a mud-for-brains Nord "What nonsense, everyone knows the Hist isn't actually a tree."

I hope this helps some, WCS. The Khajiit and Argonians, are based off Hindu, Buddhism, and Native American (Aztecs, Mayans, etc) cultures.

Edit: Also, early on in the game, (during the EP side) a Dark Elf licks the sap of a Hist and has a nervous break down, saying things like "Voices" and other nonsense. This is because he wasn't Argonian and was hearing the voices of the Hist, and likely the soul(s) he ingested. Argonians, even before licking the sap have a small connection to the Hist, as it's believed the Hist are responsible for their creation. So even as a hatchling, they're somewhat aware of the Hist. But when a non Argonian ingests Hist sap, it's like major intoxication. It's possible a non Argonian could eventually over come these effects, and commune with the Hist (likely a powerful mage). But Argonians wouldn't like it.