Manas plays multiple roles for Kumārila and it is important to keep them apart:

1. manas connecting sense faculty to ātman while sensing an external object (see ŚV pratyakṣa 160ab)

2. manas working itself as a sense faculty for pain and pleasure (see ŚV pratyakṣa 83; ŚV pratyakṣa 136ab; ŚV pratyakṣa 160 cd)

3. manas as a faculty of cognition and memory (see examples below)

Notwithstanding all these roles, manas does not, for Kumārila, work as the faculty perceptually accessing a previous cognition, as in the Nyāya and Buddhist epistemologists’ view of mānasapratyakṣa and anuvyavasāya respectively. Kumārila is quite explicit about it, see ŚV pratyakṣa 134.

Ad 1: To begin with, sense-perception according to Kumārila, works through four elements, namely the sense-faculty, its object (typically an external object), the consciousness-principle (ātman) and the manas. The consciousness-principle is needed because without it the whole process would remain unconscious. The role of manas, by contrast, is invoked in Nyāya in order to direct attention to one or the other sense-faculty and thus to explain why one may not register something although it is in contact with the relevant sense-faculty, because the manas is connecting another sense faculty to the ātman. This functioning is the reason that led scholars like Jonardon Ganeri to think of manas as covering the same role as attention in contemporary Analytic philosophy. However, whereas Nyāya authors insist strongly on the possibility of manas to only connect the ātman to one sense-faculty (so much that seemingly simultaneous perceptions are just occurring too close to each other for people to become aware of the time gap among them), the position might be less clear for Kumārila and other Mīmāṃsā authors, for reasons to be discussed immediately below and in this post: [ahampratyaya].
In partial contrast to that, Kumārila explains manas’ role in perception as primarily needed to explain the possibility of memory. In other words, if sense-perception only involved the external sense faculty and the object, there would be no way leading the sense cognition into memory (see ŚV pratyakṣa 166).
Pārthasārathi’s commentary here is explicit in saying that all memories are manas-based (sarvasmaraṇānāṃ mānasatvāt) and that therefore the possibility of remembering sensory cognitions leads one to infer that manas must have played a role in them too (ataḥ śabdādigrahaṇe ’pi manovyāpāto ’numīyate). The commentary by Pārthasārathi here also mentions the topic of attention (kiñ ca viṣayāntaravyākṣiptamanaskasya cakṣurādisaṃyukteṣv api rūpādiṣu jñānānudayād asti tatrāpi manovyāpāra iti niścīyate), but not so Kumārila himself, or at least not explicitly.
However, Kumārila appears to presuppose this view at a later point in ŚV pratyakṣa, namely in 237cd–238a, when he says that people who did not put their manas to something do not grasp things even if these are connected to their sense faculties (vimanaskā yadā ke cit sambaddham api cendriyaiḥ | na budhyante). Still, there seems to be a strong difference between Kumārila’s and the Nyāya view, insofar as —as fas as I know— Kumārila (and his commentators) don’t declare that manas can only connect one sense faculty at a time with the ātman. Rather, they use the absence of manas-connection to explain why one might not be aware of a certain object, although their sense faculties were connected to it. For instance, the absence of manas-connection explains why a person engrossed in a conversation might not be aware of the room temperature.

Manas is also said to be an indriya ‘sense faculty’ for pain and pleasure, see, for instance, ŚV pratyakṣa 83ab (manasas tv indriyatvena pratyakṣā dhīḥ sukhādiṣu); ŚV 136ab (manasas tv indriyatvena sukhaduḥkhādibuddhiṣu); ŚV ātmavāda 128 (idaṃ mamedṛśaṃ cakṣurmano me śrāntam ity api | indriyeṣv api bhedena vyavahāraś ca dṛśyate ||). Now, what happens in the case of perception using manas as the sense faculty, or manas-pratyakṣa¹ itself? Manas connects itself directly with the ātman and with its object (e.g., inner pain), without any further sense-faculty, as explained in ŚV pratyakṣa 83 cd (manasā samprayukto hi tāny (=sukhādīni) ātmā pratipadyate ||).²

In this connection, how do we grasp ourselves qua an I (I will need to come back to this topic, but see meanwhile this post: [ahampratyaya])?
Kumārila says that we grasp our self as an I through ahampratyaya and that this is a case of sense-perception. Since it is unimaginable that the self is an object of any of the external sense faculties, it appears that it has to be the object of manas-pratyakṣa. Unfortunately, Kumārila never mentions ahampratyaya in the chapter on perception of his ŚV, where the only objects of manas-pratyakṣan are sukhādi ‘pleasure and [pain]’. The self is, in contrast, identified as an object of manas-pratyakṣa later in the ŚV, in the chapter on phonemes (ŚV śabdanityatā 337–338ab: ahaṃpratyayavijñeyair ātmabhir vyabhicāritā | liṅgaśabdādyabhāvena manassaṃyogahetukam || pratyakṣaṃ caitadekāntāt sukhādāv iva kalpyate).
However, given that manas as a sense faculty should grasp a sensory object, like sukha or duḥkha, it is unclear how the aham could qualify as one. Moreover, Kumārila at times speaks of ahampratyaya as grasping the I while it is knowing. How can one understand this? Either as the claim that ahampratyaya grasps the I while it is knowing a further object X, e.g., looking at an apple, or loosely, as the claim that ahampratyaya grasps the I, which is a knower. The first position would need manas to be able to perform a double function, namely on the one hand it would work as a shift, connecting the ātman to the sense faculty, and on the other it would work also as a sense-faculty, connecting the ātman to itself and to its object, the aham.

At this point it may be important to note that there is a difference between the specific case of manas-pratyakṣa and other functions of manas. As hinted at above, Pārthasārathi is explicit in pointing out that for Kumārila the faculty of memory is manas. Moreover, manas is in charge of synthesising cognition. For instance, ŚV sphoṭa 111–115³ evokes the possibility of using manas to have a cumulative cognition of several phonemes so that one can cognise a word (this mānasa cognition seems to work like what Uṃveka ad ŚV 111 and Jayanta call saṅkalanājñāna, see Graheli 2015, tab. 7.3). Here, manas is the instrument for a cognition that is not perceptual, since it includes elements of memory, as explained in ŚV sphoṭa 117. ŚV abhāva 27 speaks of the cognition of absence as being manas-based (mānasa), exactly insofar as it presupposes perception of X and memory of Y, but it is not identical with either (gṛhītvā vastusadbhāvaṃ smṛtvā ca pratiyoginam | mānasaṃ nāstitājñānaṃ jāyate ’kṣānapekṣaṇāt ||). ŚV pratijñā 4 speaks of manas as the faculty of thinking and wishes for it not to focus on flaws only (na cātrātīva kartavyaṃ doṣadṛṣṭiparaṃ manaḥ | doṣo hy avidyamāno ’pi taccittānāṃ prakāśate ||).⁴