I'm so sorry, I know this sounds stupid, but when our pet gets "swallowed up" by the rift, they do come back, right?
Yes they do :). It will either become rift color if that species exists in rift, or it will be one of the rift monsters.
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When the feature was first introduced, they disappeared for about 2-3 days, but I believe now it's only about 24 hours or so, maybe less than that.
From RE: The Rift!
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it varies. It can be as long as three days. If you want to see that you pet still exists, it is owned by the Rift and you can find it on the Rift's userpage.
Could you link me the page?