Not sure if you recall, but Eui-Jae had said to the kid while he was in the hospital bed (in the extended flashback) that he was his "only success." So him re-iterating those words caused it to click. Like that. Hope this helped!
Also to note, they were leaving the bread crumbs. What would make someone who was experimented on [since he was a gate survivor thanks to J, which made him perfect material for Prometheus once they all believed J was dead besides our little guy], and when turned back to the time before his awakening means he would die? He had one goal in mind and that was to keep going and wait for his return like he was told to do.
Thank you
Thank you
Sorry but how did he correlate that he is that kid he cared for? It was not clear for me