Star Wars has revealed the real reason Rey scared Luke Skywalker. When Rey arrived on the planet Ahch-To, she was surprised to find Luke Skywalker an unwilling teacher. The aged Jedi Master had given up on the Force, blaming himself for Ben Solo's fall to the dark side. Luke eventually relented, but he was clearly wary of repeating his past mistakes.
In one key scene in Star Wars: The Last Jedi, Luke watched with fear as Rey dove straight into the dark side of the Force. "I've seen this raw strength only once before," he told Rey. "Ben Solo. It didn't scare me enough then. It does now." As he watched Rey, Luke became increasingly aware of some sort of Force bond between Rey and Kylo Ren - and he found that deeply disturbing.
Lucasfilm has recently published an in-universe book called Secrets of the Jedi, supposedly compiled from Luke Skywalker's notes shortly before his death. In one section he discusses the idea of Force bonds, explaining the Force can be used to mystically connect two people. "Though this may seem like a harmless - and perhaps even valuable - ability," Luke writes, "it is easily manipulated by those on the dark side. Some powerful Force users have been able to create secret bonds with others who are unaware of their connection. They then use these bonds to corrupt their target and steer their actions. Even if the unwanted bond is detected, it can still be extremely difficult to break." The text is accompanied by an image of Rey and Kylo Ren, making it clear whom Luke was thinking about when he wrote these words.
Luke could be forgiven for believing history was repeating itself. Palpatine used a Force bond to corrupt Ben Solo, one he may well have created before Ben was even born. The Emperor had watched Ben from afar, subtly manipulating him, even able to whisper in Ben's ear when he was stood next to Luke Skywalker himself. Luke was unaware of Palpatine's survival, of course, but no doubt he had spent his years of exile looking back and deducing Snoke had created just that kind of secret bond. Thus, when Luke looked at Rey and recognized the connection to Kylo Ren, he would have assumed his former apprentice was trying the same trick.
Of course, in reality Rey and Kylo Ren were not merely bonded; they were a Dyad in the Force, This concept was barely explained in Star Wars: The Rise of Skywalker, but subsequent Star Wars tie-ins have confirmed it is a natural phenomenon created by the will of the Force, that can be cultivated. The Force Dyad had not been seen for millennia, because it appears to require both the light and dark sides of the Force. As a result, neither Luke nor Palpatine had any idea what they were really dealing with.