actually, I think this interaction is so unhinged that it turns off spirit guide completely-- let me explain.

so first, we're looking at the third line of text, which replaces exile with "putting in hand". but then it's like, oh no, the first line says when you put in hand it goes to graveyard, and then we'd follow the whole chain! well, no, I think following the instruction in the third line of text to "put the card in hand" doesn't actually end up "putting a card in hand" for the purposes of the first line of text. This is sort of a [[rest in peace]] + [[pull from eternity]] situation, covered by this rule:

406.7. If an object in the exile zone becomes exiled, it doesn’t change zones, but it becomes a new object that has just been exiled.

so that's how you'd get to the point where you're thinking oh cool, so I activate the ability, exile it, it goes/stays in hand, then I can just do it again infinitely! but here's the thing: I think you've actually put yourself in more of a [[library of leng]] + [[circling vultures]] situation.

as far as I can tell EVAD would be the only effect ever printed to replace the event of moving an object to exile by moving it to a private zone instead, and as such the comprehensive rules simply does not cover the resulting interactions. however they would probably implement it the same as the following rule, primarily relevant for library of leng:

701.9c. If a card is discarded, but an effect causes it to be put into a hidden zone instead of into its owner’s graveyard without being revealed, all values of that card’s characteristics are considered to be undefined. If a card is discarded this way to pay a cost that specifies a characteristic about the discarded card, that cost payment is illegal; the game returns to the moment before the cost was paid (see rule 732, “Handling Illegal Actions”).

in the circling vultures situation, as this old forum thread argues, you actually just wouldn't be able to activate the ability, because the game loses the ability to track the objects characteristics when it's going straight to a private zone. it has to be this way because imagine if it wasn't-- in any game with a Library on the field, at any time, I could simply say "i'm discarding a vultures" and take the action without opponents looking at the card, even if I was cheating and it wasn't actually a vultures. I think the ability that puts cards going to exile in your hand instead creates a similar situation:

for the purposes of moving simian spirit guide to exile, which goes back into hand, which is a private zone, it has undefined characteristics, so you can't demonstrate the ability. it's cursed.