Adding some more context into this dialog between Oshino and Araragi will make the intent clear:
"Why would our everyday lives get turned into an anime?!"
"Because a drama CD can't convey that wonderful face you make when you act the straight man."
"It'll be fun, though. It'll be like the ending of Demon-Lord Hero Legend Wataru."
"I don't think I was even born when that was on the air!"
"You say that, but I see your Kyocera phone. The prospect is so on your mind."
(This is from Chapter 09, p.142 on the English translation published by Vertical).
Koyomi claims to be young enough not to know about a show from the late 80s, but Oshino makes the point that he's using an old man's phone (probably refers to a flip-phone, compared to the more modern smartphones; remember how Kaiki suffered when Senjougahara broke his phone).
An interesting point is that Koyomi is probably telling the truth: several sources point to the timeline of the show occurring around 2006-2007, and he would not have been born by 1989 when Demon-Lord Hero Legend Wataru finished airing.