As always, go back to the description, read it carefully, considering the meaning of each word. Often this alone can clear up confusion, or rules/mechanics that seem on their face unclear.
"When you make an attack roll while wearing the amulet, you can forgo rolling the d20 to get a 10 on the die. Once used, this property can't be used again until the next dawn."
So, when you (the player) make an attack roll (thus, any type of attack role - to-hit, melee/ranged spell-attack, etc - but not a grapple check (that is an attack (or part of and attack) that does not use an attack roll) you may choose to use this item. It does not say it requires use of an action/bonus action/reaction, so it is free to use, and need not be on your turn (so it could be used with an AoO that you are attempting to do).
Note it says "the d20" and "the die", not "the d20s", or "the dice", or "all d20s used for that attack roll", or some-such. "...the d20 to get a 10 on the die." is is singular - it applies to a single d20. So, if you are rolling with disadvantage - using two dice - two d20s, you can use a clockwork amulet to get a 10 on one of the two d20s that you are rolling. Then you take the lowest of those two. If you have two clockwork amulets then you could use them both, one per roll, to auto-get a 10 on both of the d20s. But, if you have only one clockwork amulet, it still helps - its use yields a 45% chance of getting a 1-9, and 55% of a 10, instead of the usual 69.75% chance of getting a 1-9. Without advantage/disadvantage or use of the amulet you normally have a 45% of getting a 1-9 - so the amulet does help. However, the mean roll with disadvantage and amulet use will be 7.75 instead of 10.5 (normal roll and no amulet use). So, comparing disadvantaged roll with single amulet use: same chance of 1-9, but reduced mean value.
Verdict: Use of a single clockwork amulet on a disadvantaged attack roll will reduce, but not completely eliminate the effect of the disadvantaged - which makes sense to me.