Jaimini and all commentators (with the partial exception of Śabara) agree that the eleventh book of Mīmāṃsāsūtra discusses āvāpa and tantra, which are thought of as one the opposite of the other. Jaimini uses prasaṅga just three times in book twelve (ad MS 12.1.10, 11, 15) and in a very few other instances (whereas tantra is largely employed). He might have intended prasaṅga just for specific cases, whereas Śabara systematises Jaimini's lore by classifying tantra and prasaṅga as distinct devises with specific functions and objects. That this was not just his own personal concern is proven by the text he quotes at the beginning of his discussion on prasaṅga, which also aims at distinguishing the two. It is difficult to judge about a verse, whose context is lost, however the verse might, in fact (see here) focus more on prasaṅga than on tantra. Taking into account also our data about the amount of usages of tantra as against those of prasaṅga, tantra may be in the verse no more than the common reference out of which prasaṅga is driven from, in order to better specify it. The need to go into further details as for prasaṅga could, hence, be shared by both Śabara and the author of the verse, who both needed to generalise a term whose usage was linked with specific instances but was, at the same time, not specific enough. In fact, prasaṅga is not very frequent in MS nor in Śrautasūtras, where it seems to designate the "application", possibly of a general rule. See, e.g., its only occurrence in Aśvalāyana Śrautasūtra, AśvŚrSū 1.1.22, where it is opposed to apavāda (certainly meaning "exception"):
prasaṅgād apavādo balīyaḥ
In Mylius' translation (1994:29a):
Eine Ausnahme (-Regel) ist gewichtiger als eine allgemeine Regel
The shift from this to Śabara and the verse's author meaning could be explained through a single instance in KātŚrSū (I could not locate further usages of prasaṅga in this text):
pratikarmoddharaṇam aprasaṅge (1.3.27 according to Ranade's edition)
The taking away of a brand from the Gārhapatya-fire to supply other fires [is done] for every rite, if there is no application [of a different rule] (prasaṅga).
Prasaṅga here means first of all the application of a general rule which could have already enjoined something about the uddharaṇa. If there is no such a rule (a-prasaṅga), there is the simultaneous application of the same act (of uddharaṇa) to more than one rite. Consequently, prasaṅga is seen as denoting the simultaneous application itself.
Whatever the case, in accordance with his agenda, Śabara mentions prasaṅga in his commentaries to all sūtras 12.1.1-15. After him, however, the fundamental opposition between tantra and āvāpa blurs the one just devised between tantra and prasaṅga. Hence, tantra tends to invade again the precinct of prasaṅga and to include all cases where the same element, though performed only once, applies to several cases, as against āvāpa.