When Rory turns 18, she expects to be 18 for at least five years. She doesn't plan on having already met her soulmate, on being close to him.
See, in this universe, after you turn 18 soulmates only age when they're near one another, when they're close by. The mechanics are a little odd, but in general, it means you don't age unless you know the other person, and you know them well.
But how do you know if you're aging? How can you tell that the reason why there's this one wrinkle that appears when you scrunch your forehead up is because of age and not just idiocy? How can you tell the difference between 18 and 20?
And what do you do if you notice it first, if you have a hunch that you've been aging this entire time, the entire two years that'd you been living together? Do you just casually bring it up, "Hey, I think we're soulmates and could you please remember to buy more milk later."
What if you think you're aging, and you're madly in love with this person who you're so sure is your soulmate, but then it's been ten years and you still look like teenagers? Or if your soulmate died young, or hasn't even been born yet? Then what?
So Rory doesn't have high expectations leading into her 18th birthday, but then it's two years later and she's living with her best friend and shit, they both look different, and not in a bad haircut sort of way.
/
Chase has known that Rory Landon was his soulmate ever since he was eleven and she stabbed that dragon in the eye, ever since his dream first included her, ever since she stepped foot his his life.
So no, it doesn't surprise him that they've been aging.
He knows better than anyone what it's like not to grow old. He was five for decades, but he knew that he wouldn't be 18 for long. Maybe that's why he suggested that they move in together in the first place, so that maybe she would realise that they're soulmates.
And silly him thought that she would just know immediately, that she'd grown out of her obliviousness and that maybe she'd realise that he was madly in love with her.
Spoiler alert, it took her two years and a gray hair to realise.
So yes, Chase Turnleaf knew from the start that he was growing old, and he didn't mind it at all.