Short answer. Yes. Article 642 of the Civil Code gives you the right to make water flow through intervening estates to reach your property, but it comes with the obligation to indemnify not only the owners of those intervening estates, but also the owners of the lower estates upon which the water may filter or descend.
What the law says
Any person who may wish to use upon his own estate any water of which he can dispose shall have the right to make it flow through the intervening estates
Civil Code, Article 642 — The Right to Make Water Flow Through Others' Land. Read the full provision →
What the law says
with the obligation to indemnify their owners, as well as the owners of the lower estates upon which the waters may filter or descend
Civil Code, Article 642 — The Right to Make Water Flow Through Others' Land. Read the full provision →
The right to channel water comes bundled with an obligation
Article 642 grants the right you are relying on: any person who may wish to use upon his own estate any water of which he can dispose shall have the right to make it flow through the intervening estates. But the same sentence that gives you the right also attaches a condition to it. The right to channel water across your neighbor's land is not free of obligations to the people affected by that water once it is flowing.
Two groups of owners are named, not just the one you cross
The article is specific about who must be indemnified, and it does not stop at the land your pipe or channel physically passes through: with the obligation to indemnify their owners, as well as the owners of the lower estates upon which the waters may filter or descend. That second group, the owners further downhill where the water eventually filters or descends, is named separately, alongside the owners of the intervening estates your water actually crosses.
Why the law reaches beyond the estate you cross
Water does not necessarily stop where your channel ends; it can continue to filter or descend onto land beyond the estate you crossed. Article 642 accounts for that by extending the indemnity obligation to those lower estates as well, rather than limiting it to whichever landowner happens to sit directly along your chosen route. The obligation follows where the water actually goes, not only where you routed it.
What this means for you
Since you are channeling water across your neighbor's land to reach your property, Article 642 answers your question directly: yes, the owners of land further downhill where that water eventually drains are covered by the same indemnity obligation as the neighbor whose land you cross. Both groups of owners fall within what the article requires you to account for once you exercise this right.