McDonnell, Kilian & Montague, George T. "Chapter Nine: Tertullian: Montanism and Reluctant Withdrawal of Communion." Christian Initiation and Baptism in the Holy Spirit: Evidence from the First Eight Centuries. Collegeville, MN: The Liturgical Press, 1991, 106-121.
McDonnell had previously observed a decrease in the emphasis on charisms in the church. Here he ties it to the growth of Montanism, which held a strong interest in the spiritual gifts (McDonnell & Montague 1991, 106). Tertullian himself became a Montanist, which may have a bearing on our understanding of his work on baptism.
Montanism arose in the third quarter of the second century, though McDonnell admits reports of the year do not agree (McDonnell & Montague 1991, 107). It became a relatively popular idea in North Africa. At first, there were attempts to be conciliatory with the movement. However, in Asia Minor the church went so far as to call councils to deal with problems which arose (McDonnell & Montague 1991, 108). Meanwhile, Tertullian found the new bishop of Rome to consider Montanism to be received peaceably, as part of the Christian communion.
McDonnell observes that Montanism had a diversity of expressions. It was eventually condemned by Rome due to "abuses and excesses" (McDonnell & Montague 1991, 109) by sometime early in the third century. Though prophecy clearly was a part of Christian experience in the apostolic age and for some time afterward, there were always problems with false prophets and a failure to judge prophecy adequately against Scripture (McDonnell & Montague 1991, 110). McDonnell concludes that the condemnation of Montanism with its emphasis on spiritual gifts would have "made it difficult to support prayer for charisms within the rite of initiation" (McDonnell & Montague 1991, 110-111).
McDonnell questions whether Tertullian is suspect because of his move toward Montanism, and particularly whether his view of baptism is trustworthy. He converted to Christianity around 190-195 and wrote his On Baptism rather early, with five or six books after it before showing Montanist tendencies (McDonnell & Montague 1991, 111). On Baptism seems squarely catholic in its ecclesiology.
Eventually, Tertullian left Catholicity to be a Montanist, then left Montanism for a sect of his own founding (Augustine, On Heresies 8:6). McDonnell recognizes Tertullian as a brilliant writer (McDonnell & Montague 1991, 115).
It is not surprising that a character like Tertullian would provoke responses from others in and after his period. Cyprian of Carthage regularly read Tertullian and drew on his ideas (McDonnell & Montague 1991, 118). Hilary of Poitiers made specific references to Tertullian but did not consider all his works equal. Augustine considered Tertullian a heretic of the first order. Jerome would commend Tertullian as a genius but condemn his heresy (McDonnell & Montague 1991, 119).