As far as Arakkii mutants being resurrected goes, when Way of X had the threat of one of Mars' moons being about to crash into it, there were a couple panels about how - as Krakoa/SWORD/Kurt all tried to figure out ways to save as many Arakkii as possible in case they couldn't stop the moon - 'the Quiet Council hastily attempted to renegotiate Arakkii participation in the resurrection protocols, but the Arakkii just laughed at them.'
The impression I got was that Cerebro DOES in fact back up the Arakkii, same as any other mutant on Earth (there's no reason for the machinery to differentiate between an Arakkii mutant and a Krakoan one after all, and Arakko spent its first few months back on Earth before the terraforming of Mars, so even if distance was an issue, there'd be at least back-ups only a few months old, from when Arakko was sitting just off the coast of Krakoa). And now with the Waiting Room, I presume Arakkii souls/consciousnesses are drawn to the Waiting Room after death the same as Krakoan ones.
The only difference is the Arakkii over all seem to have no interest in resurrection. They like the finality of death, the meaning/urgency it gives to life. Like, they probably CAN be resurrected by the Five just as easily as anyone on Krakoa, but at some point they made it clear they have no desire as a society on the whole, to be added to the resurrection queue (per the idea that for REnegotiations about Arakkii resurrection to have happened in Way of X, an initial offer had to be first extended, and turned down by the Arakkii leadership at least). So the Five simply don't consider Arakki back-ups - though they no doubt exist - as being part of the resurrection queue, until asked to do so.
And similarly, with the Waiting Room, obviously nothing explicit has been said but I can't imagine Wanda designing it without allowing for mutant souls to have the OPTION of not waiting around to be resurrected but to simply pass through it onto whatever afterlife 'comes next.' And my assumption, until stated otherwise, is that Arakkii are drawn to the Waiting Room after they die now, same as Krakoans, they just tend to not linger and just pass on through it.
Course, just because that's the OVERALL Arakkii view of resurrection, that doesn't mean there's not going to be exceptions. We already know of at least one - in Wolverine's solo series, Solem took up residence on Krakoa and specifically negotiated with Emma to get himself added to the resurrection protocols. He doesn't give a fuck what the rest of his people think of him and he's the kinda character who's like 'eh, I would like to reserve the option to just....not be done being alive until I'm good and ready to be done with that.'
I imagine that at some point in the future, we might start to see some Arakkii individuals making the choice to use the Waiting Room to get added to the queue, and return to life, even if its not socially accepted in their own society.....they always have the option of Krakoan society instead, much like Solem. Just as there's inevitably going to be at least some Krakoans who don't actually want resurrection, like in the cases of mutants with predominantly human families, who don't want to outlive their siblings/spouses/etc and prefer to limit themselves to a lifespan comparable to the rest of their family's.
But as for Tarn, right now.....I don't think we've seen the last of him, because much like Solem, this is another guy who doesn't actually give a fuck if the rest of his society hates or judges him....and he's been very clear he's not interested in dying any time soon. He was trying to yield to Magneto the second he realized he was screwed, and he wasn't willing to risk Storm being able to kill him before he could finish off her in their duel.....nah, this is not an Arakkii who is okay with exiting stage right before HE decides he's done. And Tarn wasn't looking to die today. Not by a longshot.
Course, I don't think this means he'll end up in the Krakoan resurrection queue - we're talking about the Arakkii version of Sinister, as others have pointed out. There's no WAY he doesn't have his own failsafes in place in case something like this DID take him by surprise, or some clones of his own stashed away ready to awaken if Tarn the First happened to get Julius Caesar'd on his way to the Senate one day.
Anyway, that's just my assumptions about the current state of potential Arakkii resurrections, and Tarn's in particular.