Here is the situation:

• +40 year old convert from the Presbyterian sect.
• Baptized in the Presbyterian sect as an infant.

• Proof of baptism: Witness (mother) and a certificate. No other evidence available ( video, minister affidavit, et)
• Received into the Catholic Church via Novus Ordo RCIA
• RCIA did not require conditional baptism because the witness and certificate suffices, no negative doubt.
• Presbyterian baptism matter and form do align to the Catholic rite. However, Presbyterian do allow applying the water by aspersion (sprinkling). In fact, aspersion is the most common application vs. pouring water or immersion.

Case for no conditional baptism:

• No positive doubt. The Catholic church recognizes that anyone can minister a valid sacrament and the Presbyterian sect baptism follows Catholic requirements.

Case for receiving conditional Baptism:

• Positive Doubt does exist with the  Presbyterian rite. Water Baptism by aspersion does not guarantee that the water would flow over the head. The flowing of water is necessary for it to be valid.
• Prior to Vatican 2 the Catholic Church had always required conditional baptism for protestant converts because of the impossibility to investigate such baptisms. You can find this claimed by Novus Ordo and Protestant apologetics as well as pre-Vatican2 sources. Novus Ordo and Protestant sources admit that Vatican2 church change the approach to to receiving Protestant converts.
• Some very well known former Presbyterian ministers converts received conditional baptism.
• Another famous example, John Henry Cardinal Newman received conditional baptism after converting to the Catholic Faith from the Anglican sect.

Based on what I have provided, would you lean towards  a conditional baptism or not and at what confidence level? Or is this something so complicated that we simply have to rely on the counsel of a priest?

From the 1917 Code of Canon Law

The Sacraments of Baptism, Confirmation and Orders which imprint a character cannot be received a second time. If, however, there is prudent doubt whether they have been received, or whether they were validly received, they may be conditionally repeated. (Canon 732.)

When Baptism is repeated conditionally, the same sponsor should, if possible, act who was present at the first Baptism; outside this case, there is no need of a sponsor in conditional Baptism. In the repetition of Baptism under condition, neither the sponsor of the first, nor the one at the second Baptism contract spiritual relationship, unless the same sponsor was present at both Baptisms. (Canon 763.)


From Denzinger:
LEO XIII 1878-1903

The Reception of Converted Heretics
[From the Decree of the Holy Office, Nov. 20, 1878]

1848. To the question: "Whether baptism should be conferred conditionally on heretics who are converted to the Catholic religion, from whatever locality they come, and to whatever sect they pertain?"

 The reply is: "In the negative. But in the conversion of heretics, from whatever place or from whatever sect they come, inquiry should be made regarding the validity of the baptism in the heresy which was adopted. Then after the examination has been established in individual cases, if it is found either that none was conferred, or it was conferred without effect, they shall have to be baptized absolutely. But if according to circuмstances and by reason of the localities, after the investigation has been completed, nothing is discovered in favor either of validity or invalidity, or, probable doubt still exists regarding the validity of the baptism, then let them be baptized conditionally, in secret. Finally, if it shall be established that it was valid, they will have to be received only for the profession of faith."