Tertullian, a Montanist, believed in baptism of believers by immersion, not sprinkling

The following paragraphs are excerpts from Tertullian’s work, Concerning Baptism, written some time in the late second or early third century. It is almost certain that Tertullian authored this work before he became a Montanist.¹See http://www.tertullian.org/chronology.htm for a suggested chronology  This is significant because it means that the practice of dipping/immersing repentant converts did not originate primarily from the Montantists, but rather from within the Church at large. This mode of baptism seems widely practiced even outside of the movement.

(The title headings and emphasis in the quotes below are added)

Baptism by immersion is an afterthought to Tertullian

But it will be enough at the outset to seize upon those features in which the essential character of Baptism is recognised. Its first aspect is that by which even in those days the very attitude gave an early indication of the manner of Baptism, namely that “the spirit of God,” which from the beginning “moved upon the” primal “waters,” would rest over the waters of Baptism. Moreover, it was certainly a holy thing that moved over what was holy, and the supporting waters borrowed their holiness from that which moved over them. Every underlying substance must catch the quality of that which is suspended over it, particularly when the former is corporeal and the latter is spiritual, as the spiritual by the fineness of its substance can easily penetrate the corporeal, and also settle in it. So the nature of the waters, having been made holy from that which is holy, has itself also conceived the power to sanctify. Let no one say: “Are we really dipped in the very waters which existed then in the beginning?” Not, of course, the very waters, except to the extent to which, while there is one class, there is a number of subdivisions. What belongs to the class extends also to the subdivision. Therefore there is no difference whether one is washed in the sea or in a pool, in a river or in a spring, in a lake or in a river bed, and there is no difference between those whom John “dipped in the Jordan” and Peter in the Tiber, unless it be true also that the eunuch whom Philip baptized on his journey with such water as offered, obtained more, or less salvation than others. Therefore all waters by virtue of the old privilege belonging to their origin, obtain the mystery of sanctification after God has been invoked. For immediately the Spirit comes from heaven over them, and is above the waters sanctifying them from itself, and being thus sanctified they imbibe the power of sanctifying. And yet the parallel would accord with the simple act, namely that since we are stained by sins as if by filth, we may be washed by the waters. But although sins do not appear in the flesh (since no one bears on his skin the stain of idolatry or rape or fraud), yet their like are foul within the spirit, which is the originator of sin. For the spirit is lord, the flesh is its slave. Yet both share the guilt with one another, the spirit because of its command, the flesh because of its obedient service. Therefore when the waters have been, treated in a certain way by the intervention of the angel, the spirit is bodily washed in the waters and the flesh is spiritually cleansed in the same.

Modes of baptism (Immersion and Sprinkling) contrasted by Tertullian

But you will tell me that peoples without the slightest understanding of spiritual things attribute power to their images of gods through the same efficacy in water. These, however, deceive themselves, since the water they use is bereft of spiritual power. For they are initiated into certain sacred rites by a bath, those of some Isis or Mithras; even their very gods they exalt with washings. Indeed, it is a universal custom to carry water round estates, houses, temples and whole cities, for their purification by sprinkling. It is true that at the celebrations in honour of Apollo and those held at Pelusium, worshippers are dipped, and they have the effrontery to declare that their object is rebirth and an escape from punishment for their broken oaths.

Similar to the Didache, Tertuallian remarks that the recipients of baptism are the repentant, not infants

Those about to enter on Baptism should supplicate with frequent prayers, fastings, genuflexions and vigils, and with confession of all their past sins, that they may set forth the baptism of John also: “they were baptized,” we are told, “confessing their sins.” We must be congratulated if we now in presence of the congregation confess our iniquities or meannesses. For we are at one and the same time both making an apology for the past with a struggle between flesh and spirit, and raising up beforehand defences against the trials that are to follow. “Watch and pray,” he says, “lest ye fall into a testing situation.”