Every GM will have a different interpretation on how this works. You just have to find out and play along. Unfortunate but there is no solid rule answer.

Not official ruling, but perhaps this tweet from the Dev may be interesting for this thread:

@DerynDraconis Can a creature with Tremorsense locate player while he is moving, with a successful Dexterity (Stealth) check, within its radius? Or a success is impossible because vibrations (including heartbeats or breathing) prevents a player to move stealthly vs Tremorsense?

@JeremyECrawford Tremorsense doesn't automatically nullify someone else's Stealth. It lets you notice someone in contact with the ground on the other side of a wall, for instance. But a person can still move stealthily enough to escape the notice of a creature with tremorsense.

Knowing somebody is present doesn't mean it is a targetting sense.

In my game it would be because I like to keep things simple, but in other GM's games it might not be.

My 2 cents as a perspective to make things make sense thematically, mechanically and scientifically.

Black flames do exist in the real world, although they take chemicals that need to be combined in a specific way. Check that out online so you have an idea of what "shadow-like flames" could be like. Imagine a rock in a bonfire, and invert the colors for example. The rock is still obscured no matter what color the "flames." I think the "flame-like" part of that might just refer to a shape in this case.

That being said, in my brain, I don't think Shadow of Moil is creating shadow so much as removing light. THAT'S why it gives light a "level" of dimming around them. This would explain why they are obscured and Truesight can't get through it. Light has to hit and reflect in some way for sight to be useful. If the light never gets to the object then you can't "see" it. Just like radar jamming, just for your eyeballs. Something is absorbing light all around the caster and VERY little light is getting to the caster and getting back to the baddies eyeballs. This along with the constant motion that is related to the "flame-like" description, means that this is a non-magical obstruction that can't be "seen" through because no light gets through or reflected off of these "flame-like phenomenon. Which is also why blindsight and tremor sense might be used since they don't rely on "sight"

If you have a window that absorbs all light, you can't see through it. It's not illusion, it's not shadow, it's an absence of actual light. The REVERSE of a torch. Instead of creating light it's eating it. Or a black hole. Light goes in and it doesn't come out. You can't see through it. So I believe tremor sense and blindsight would both work but not Truesight.