Everything in the CS is server-wide, why would it be different for the DLC's?
It's kinda logic imo, though it makes sense to ask for it to be account wide. The only way to do so at the moment it to buy them outside the CS, when they release bundles like the ESO: Gold Edition, it's account-wide in that case, just like crowns and ESO Plus bought outside the CS are account-wide as well.
If you play on both severs, you might find ESO Plus worth it as it unlocks all the DLC's on both of them, that way you could also use your extra crowns to buy something else.