As seen in the screenshot above, OR/AS Tutor moves on Power Construct Zygarde is considered illegal by Pokemon Showdown, however, I found out not too long ago, that it is actually legal for Zygarde to have both OR/AS Tutor moves and Power Construct.
A Zygarde that is caught in X/Y can be transferred to OR/AS and then learn the moves it wants to learn there, and then it can be transferred to S/M. Of course the Zygarde will have Aura Break when it is first transferred, but it is possible to change the ability of Zygarde from Aura Break to Power Construct once transferred. If you have collected all 100 Cells and have 50 or more usable cells in the Zygarde cube, you can assemble a Zygarde from the one with OR/AS Tutor moves and the 50 cells from the Cube to upgrade the Zygarde to a Power Construct one, where it'll keep its moveset, nature, IVs, etc.
I know Battle spot isn't exactly the most trustworthy place to show what's legal and not, but here's a battle with a Power Construct Zygarde that knows iron tail on a Battle Spot Free Battle anyway: V8VG-WWWW-WWW6-LHS6
So what does this mean for Zygarde's compatibility with OR/AS Tutor moves as a whole? Well here's an overview:
Zygarde 50% Aura Break: Legal with OR/AS tutor moves and TMs
Zygarde 50% Power Construct: Legal with OR/AS tutor moves and TMs
Zygarde 10% Aura Break: only Legal with S/M Level up moves, TM and tutors
Zygarde 10% Power Construct: Legal with OR/AS tutor moves and TMs
Note: Zygarde 10% Aura Break is not legal with OR/AS Tutor and TMs, because unless you upgrade it to Power Construct, you can only upgrade a Zygarde 10% with to the 50% form, not the other way around. Zygarde 10% with Power Construct is legal with Tutor moves, because the Zygarde Cube allows you to switch between the 50% and 10% form of a Power Construct Zygarde at will, outside battles.
Edit: I've seen something similar posts about Zygarde and Tutor moves before, but I'm not sure if they made this clear. Also, I forgot to mention that it's impossible to chance a Zygarde with Power Construct back to Aura Break, so that's
not a method that could be used to get a Zygarde 10% with OR/AS Tutor moves.