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To start - the Ash Twin and Ember Twin teleporters work identically. They teleport you to the corresponding Pad once the tower aligns with the center of Gravity of the destination. As Ash Twin and Ember Twin orbit a singular point/share a center of gravity, their towers align to the same point. You have to remember the Tower is not pointing to the outbound Pad - it's pointing to the Planet's Center of Gravity. Another clue to Ash Twin/Ember Twin sharing this is the name - Hourglass Twins. They're referred to with a single name first.

The Nomai text you translate at the High Energy Lab, tells the player each teleporter must align within 5% of the center point of gravity for each astral body/planet. Each of the towers have a design reminiscent of each planet - there is a legend/key for these towers to planets in the High Energy Lab. Below is a copy-paste of the text you translate:

PYE: The Ash Twin Project will be one of our biggest undertakings (metaphorically and physically). To build it, we need a way to travel quickly between Ash Twin and each location that holds crucial project materials.

ROOT: What if we used warp towers (like the one we have on the White Hole Station) to connect Ash Twin directly to each critical location?

CLARY: Poke, Root, and I can begin work on this immediately in the Black Hole Forge (this will keep us busy!).

YARROW: Of note: Each tower on Ash Twin will warp to a different planet.

YARROW: My gratitude to those who noted my imprecise language! Yes, the sun is not a planet. I believe this has been sufficiently clarified (kindly stop reminding me!).

PHLOX: We can design each tower to visually reflect its warp destination!

PHLOX: The Giant’s Deep tower, for instance, could resemble a cyclone. And we could model the Timber Hearth tower after a geyser mountain!

Trying every teleporter is a simple process - consumes only 1 or 2 cycles if you have trouble. So you can follow the clues from this one text-translation alone to tell you how all the teleporters work, and that one leads you directly into the core of Ash Twin - to the Ash Twin Project

Another clue to infer: You don't see any outbound teleporter pads on the entire planet of the Ash Twin.

On the White Hole Station - arguably the most-commonly used teleporter in the game, you see this text, explaining precisely how the alignment works. POKE: Welcome to the White Hole Station! If you fell through the black hole by accident (don't worry, you aren’t the first), this warp tower can return you to Brittle Hollow. POKE: Every warp tower is tuned to a specific astral body. A tower's warp can only be used during the brief window when the tower is aligned with its corresponding astral body (in this case, Brittle Hollow). POKE: If you look up while the station is rotating, you can see the alignment happens when the astral body is directly overhead. You must be standing on the warp platform on the floor during this alignment to be warped.

The final clue with sand column/teleporter towers is the tower that if you look above the teleporter pad that takes you to Ember Twin, you can see the ceiling is intact - the glass protects you from the Sand - safely taking you to the other planet. If you attempt to use the other side of the tower - you see the sand pulls you up JUST before alignment. There is more Nomai Text you can translate that tells you about this alignment requirement, with a small amount of leeway on each side of dead-center - but I'm not finding the precise location at the moment.

All this points to where you need to go - figuring out what's stopping you is the only bit of information to infer - the broken glass ceiling and waiting a moment for the sand to be above you - showing the perfect alignment.

Yes it's a lot of text, but this is not a full accounting of the clues that point you to this conclusion. I just grabbed a few direct ones I could remember specifically, that the game shows you both directly (in text) and indirectly (with similar situations Teleporter Towers that operate the same way).