The Effeeti grants the ability to cast wish spells
If you look at the Spell Like Abilities section of the Efreeti, it looks like this:
Spell-Like Abilities (CL 11th)
Constant—detect magic
At Will—plane shift (willing targets to elemental planes, Astral Plane, or Material Plane only), produce flame, pyrotechnics (DC 14), scorching ray
3/day—invisibility, quickened scorching ray, wall of fire (DC 16)
1/day—grant up to 3 wishes (to nongenies only), gaseous form, permanent image (DC 18)
All1 the abilities are spell effects, and the wishes are also italicized, as it standard notation for indicating spells. That is a pretty clear clue that these are wish spells. The reason this is written so strangely is because the Efreeti cannot itself cast wish spells, it only can grant up to three wishes to nongenies who ask for them. The grantee then can formulate their wishes and cast the spells.2 Granting the wishes is a standard action according to the rules for spell-like abilities:
Using all other [i.e. not Constant] spell-like abilities is a standard action unless noted otherwise, and doing so provokes attacks of opportunity.
The grantee then speaking all three wishes would take at least another 3 standard actions, because the casting time of wish is also a standard action. How long the grantee can wait between wishes is not further specified, and up to the DM.
1 Invisibility, for some weird reason is not italicized on AoN. Apparently this is a formatting error by AoN, and it is in italics in the print version; thanks to @williwontu.
2 For example, there is a whole adventure path, Legacy of Fire, that revolves around an Effreti's plan to overcome the inability of Efreet to formulate wishes themselves. From the introduction of the last installment, "The Final Wish" (p. 7)
So the powerful efreeti turned his attention back to his
original plan—to use his own wishes, siphoned through
mortal lips, to absorb and infuse himself with the essence
of a great monster of yore
and on p. 56
Such tales exaggerate much, but at their root lies a single
undeniable truth: some genies can grant wishes. Blessed with the might to reorder reality, yet cursed never to take advantage of their own powers, genies both take pride in their incredible ability and resent that their gift can only serve the wills of lesser creatures.
and p. 57
Regardless of how they come by their powers, though, genies
possess one law that rules over their ability: no genie may
grant wishes to another genie, especially themselves.
wish makers who entreat genies to perform tasks that
could naturally occur are more likely to find their wishes
granted as they desire, while those who presume to make
wild demands of reality often find themselves thwarted by
offended genie wishcrafters
That is, the genie grants the power to the nongenie to make wishes, the nongenie then casts those wishes (note the wish in "wish makers" is in italics). And all the grantee has to do is to speak their wish to cast it. As per the spell's description:
Wish is the mightiest spell a Wizard or Sorcerer can cast. By simply speaking aloud, you can alter reality to better suit you.
And it then is the genies inherent ability to fullfill the wish that has been cast, or thwart it if it is overreaching. (At traditionally done for wishes by the DM, who plays the genie).
I think this is not fully mechanically sound, because what happens if the genie dies after it granted the power to make those wishes? But that probably needs to be resolved by the DM, and also is not the focus of the question here, the question is about the action economy of the wish-granting spell like ability. And that just is a standard action, without the genie casting any whishes at that time.