Short answer. No. Article 584 exempts a donor who has reserved the usufruct of the property he donated from the security requirement that would otherwise apply to a usufructuary. You may enjoy the usufruct you kept for yourself without first posting that security.
What the law says
The provisions of No. 2 of the preceding article shall not apply to the donor who has reserved the usufruct of the property donated, or to the parents who are usufructuaries of their children's property, except when the parents contract a second marriage.
Civil Code, Article 584 — Who Is Excused From Security. Read the full provision →
The exemption applies to exactly your situation
Article 584 is titled around who is excused from security, and it names your situation specifically: the provisions of No. 2 of the preceding article shall not apply to the donor who has reserved the usufruct of the property donated. The preceding article sets out the ordinary requirement that a usufructuary give security before entering on the enjoyment of the property. Article 584 removes that requirement for a donor in your position, someone who gave away the property but kept the usufruct for themselves.
Why a donor-usufructuary is treated differently
The security requirement exists to protect the person who will eventually receive the property free of the usufruct, ensuring the usufructuary does not waste or damage it. When the usufructuary is also the donor, the underlying concern is weaker: the donor already owned the whole property outright before making the gift, and reserving a usufruct over what was once fully theirs is a very different situation from a stranger being handed the right to use someone else's property. That difference is what the exemption in Article 584 reflects.
The article covers a second group as well
Article 584 extends the same exemption to another category: "or to the parents who are usufructuaries of their children's property, except when the parents contract a second marriage." Parents enjoying a usufruct over their children's property are likewise excused from posting security, for reasons rooted in the trust the law places in the parent-child relationship. That trust has its limits, though: the exemption disappears specifically if the parent enters into a second marriage, at which point the ordinary security requirement is restored for that parent.
What this means for your donation
Because you reserved the usufruct for yourself when you made the donation, Article 584 places you squarely within the exempted category. You are not required to post security before enjoying the usufruct you kept, unlike a usufructuary who received that right from someone else entirely. This exemption is personal to your position as the donor who reserved the usufruct, so it is worth keeping documentation of the donation and the reservation clear, in case the exemption is ever questioned.