Ok, big question here, where are these pieces from? Wowhead states from Heroic VOI, pls see link, and yet when I go to VOI either on Wowhead and/or the Adventure Guide in game play, I see for example the helmet drop from Heroic VOI is this piece which stinks…[item=195476]. I’ve farmed VOI a few times no drops so I can’t be sure so I’m asking the world if WOwhead and the Adventure Guide is wrong, thx!!!
Vault of the Incarnates Heroic Shaman Set - Transmog Set - World of Warcraft (wowhead.com)
So the thing about tier set appearances in DF raids is that instead of providing all the pieces of a set appearance as boss drops, Blizzard planned around the existence of the catalyst, and many appearances are only available from catalyzing a different piece into the tier set appearance, which I hate because all catalyzed items are class-specific, and therefore unmoggable for any other class. 
For the Heroic Vault tier appearance, you will need to collect non-tier mail items from Heroic Vault on a shaman, and then catalyze them into the shaman set.
So question, if I purchased Mythic BoE items from Dragonflight raids could I then use the Catalyst to convert them into mythic tier sets without ever doing the raid itself?
Yes.
10 char
What do you mean catalyze and where does one do that?
Dorn has a catalyst, since it’s the past tiers, you should be able to upgrade for free if you provide the appropriate item.