Q: How do the Relic "talents" unlock?
A: As your Artifact increases in level (by spending Artifact Power), your Relic slots will level up as well. When you first unlock the Crucible, you'll have access to the first additional trait (a +5 increase to your Artifact's item level) in each slot. The second row unlocks at Artifact level 60, 63, and 66 (for the left, center, and right Relic slots respectively), and the third and final row unlocks at Artifact level 69, 72, and 75. This should all be pretty apparent when you look at those slots in-game, but may not be showing clearly via datamined info.
Q: What did you mean by "it can't double roll a trait"?
A: Just that you will never be able to upgrade a Relic to increase the same Artifact trait twice. If your Relic already has a bonus rank of Wrath of the Ashbringer on it, that trait will not be one of the three options presented in the bottom row of the Crucible's upgrade tree.
In other words, there's no risk of having your Wrath of the Ashbringer relic be "ruined" by not rolling a second bonus to Wrath of the Ashbringer, because that could never have happened in the first place. However, if you get a relic without Wrath of the Ashbringer, there's now a chance that it'll gain it from the Crucible.
Additionally, those three options will always be unique; it won't, for example, give you the "choice" between Deflection, Deflection, or Deflection. Aside from making sure you always have options, this means that your odds of having your favorite trait appear on a Relic you'd otherwise have discarded are actually pretty decent.
Q: How do the ranks for the first two rows work?
A: There are no such ranks. We think this is coming from some confusion about how the Netherlight Crucible is showing up in datamining, versus how it actually operates in-game. Once you've unlocked a row in the Crucible, you just select the option you like, and that's it - there's no additional leveling up of those options beyond that.
For those peeking into the data (or anyone else who might be curious): this is because of how we built the system to allow the unlockable effects to stack between each relic. It's just a subtle behind-the-scenes optimization on our end.
Hopefully that will help clear the air about how the Netherlight Crucible works, but we're sure you have more questions, so ask away and we'll do our best to answer what we can! We'll aim to provide an update sometime next week. Thanks!