The adjective parinibbāyī isn't temporally stipulative at all.
Suppose Pukkusāti had been an upahacca-parinibbāyī (as the Majjhima Atthakathā claims) and had already attained arahatta at the time of the Dhātuvibhangasutta. Or suppose he'd been one of the more sluggish kinds of anāgāmī and had not yet attained arahatta. Either way he would still be denoted parinibbāyī.
And so in contrast with the past participle parinibbuto or the future tense finite verb parinibbāyissati, the word parinibbāyī conveys no information as to whether Pukkusāti's arahatta has already happened or has yet to happen. It tells us only that he's someone who has attainment of it as his destiny in that particular life.
A very literal rendering:
Note that I've taken the adverb tattha as being used in its temporal sense rather than its locational or spatial ones: "in due course", "eventually", "sooner or later".Pukkusāti, bhikkhave, kulaputto pañcannaṃ orambhāgiyānaṃ saṃyojanānaṃ parikkhayā opapātiko tattha parinibbāyī anāvattidhammo tasmā lokā”ti.
"Pukkusāti, monks, a son of good family, on account of destruction of the five fetters that partake of the near shore, is one of apparitional arising [in the Pure Abodes], one to be in due course fully extinguished, one whose nature is not to return from that world."