Spoilers please don't read if you didn't read novel
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I think it didn't matter if he was not a pivot in the second or was. He was still one in the first TL, plus it took a lot of energy and had a big impact on everything basically.(I also dont know how far are you in the novel or if you ended it so I'm trying to be considerate with details)
It was just another like, consequence, or rather anomaly haunting him down because of the going back. That's how I think. I hope i didn't forget anything else regarding this one though. If I'm off someone correct me
Spoilers (will cover the later parts of the novel)
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J is not the anchor for the 2nd timeline (bc he died), it was Sayoung. However, TL2 Sayoung's powers weren't enough so he got the side effects, which was becoming a warden after his world ended.
Now the West Sea Rift is essentially the remnants of TL2's world. When TL3 J went inside, it closed because it was trying to find him, who was the original anchor (since TL1 J was the original).
Think of it like TL2 Sayoung wasn't enough so it tried to find J so it can "punish" him instead.
Spoilerr (also there should be a delete option and no offense towards you)
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I don't think it's about the watch because it was more of a trinket that connected these two tls. If I'm not wrong, if it was indeed what made him go whoop into the rift then the rift would have to open again when he was wearing the watch later on me thinks
Unfortunately no, you can't delete a comment so it's like, unless it's not covered in mass comments above or just skipped over then ppl are gonna see it. But oh well it's fine, don't worry, I think whoever sees the convo abt spoilers will (hopefully) skip it bc I usually just scroll pretty fast when I don't wanna witness the obvious spoilers. Everyone makes mistakes shit happens. Although sorry it's not an answer you would like to read about

SPOILER WARNING
This is one thing I don't understand why the rift close when J entered when is he not the anchor of 2nd timeline??