Bugaeva (2010: 752) sums up prototypical applicatives as follows:
The applicative is typically described as a syntactic construction signaled by
overt verbal morphology which allows the coding of a semantically peripheral
argument or adjunct as a core object argument (Peterson 2007: 1; cf. Comrie 1985:
III-316, Spencer 1991: 253, and Polinsky 2005: 442). This newly introduced object
argument is usually referred to as an applicative object (henceforth AO).
The above definition implies that, a prototypical applicative construction has
the following three properties:
- An applicative construction increases verb valency by one.
- An applicative construction provides an alternative to oblique realization of
a semantically and syntactically peripheral participant, i.e. there must exist a
non-applicative (base) construction.
- An applicative construction does not involve non-peripheral participants,
such as Agent and Theme/Patient. Addition of an Agent typically results in
causativization; likewise, addition of a Theme/Patient results in non-causative
transitivization.
Applicatives therefore wouldn't ever govern a case other than accusative (or however direct objects are marked). What they do do is take some peripheral or oblique argument (like a location or benefactive) and make it into a core argument (specifically, a direct object). Here's an example and its non-applicative paraphrase from Ainu (from Bugaeva 2010: 753):
(1)
a. casi upsor ta ahun=an ruwe ne
castle inside to enter.SG=IND.S INF.EV COP
‘I entered the castle.’
b. casi upsor a=Ø=o-ahun ruwe ne
castle inside IND.A=3.O=to.APPL-enter.SG INF.EV COP
‘I entered the castle.’
In (1a), casi upsor takes the postposition ta, which indicates it is an oblique argument, specifically, a location. However, the applicative paraphrase in (1b) doesn't have the postposition, and instead has the locative applicative morpheme o-. Additionally, Ainu has no case marking but has the strict word order of SV in simple intransitive clauses, and SOV in simple transitive clauses. This means that casi upsor here is likely the direct object. This is also backed up by the verbal agreement marking. In the indefinite person, like we have here, Ainu has a tripartite system, with the subject of transitive clauses, the subject of intransitive clauses, and the direct object of transitive clauses each being marked differently (a(n)- for A, -an for S, and i- for O). We see the overt agreement suffix here being the intransitive one, -an in the non-applicative paraphrase, and the transitive one, a(n)- in the applicative version.
Pylkkänen (2002) looked at the similarities between "true" applicatives, like those that are found in Ainu, and double direct versus dative ditransitive verbs in English through a minimalist framework and found some fundamental differences, terming the former "high applicatives", and the latter "low applicatives". For instance, you cannot add a benefactive participant to an English unergative verb, but you can in the Bantu language Luganda:
(11)
c. I ran.
d. *I ran him. [meaning ‘I ran for his sake’--my addition] (Pylkkänen 2002: 17)
(31)
a. Mukasa ya-tambu-le-dde Katonga
Mukasa PAST-walk-APPL-PAST Katonga
‘Mukasa walked for Katonga’ (Pylkkänen 2002: 25)