There are no rules to this, if the relationship seems to be going that route where it “has to be done by a certain time,” it’s probably not a genuine one anyway, b/c one or both people are doing/wanting what’s expected rather than what comes naturally.
Also, don’t discredit someone just because they didn’t call you within one week. I can think of three things here:
1. You should have just as much desire/obligation (if there is one) to call HIM within a week. The type of relationship you seem to want isn’t a game where it’s “someones turn” to call.
2. I just spoke to a friend who was going through a similar situation and turns out the guy didn’t call for a week b/c he’s a radio personality who is also heavily involved in philanthropy (So he was just plain busy). I told her to call him instead . . . she did, and they’ve been talking ever since.
3. You met him on an online dating site. He’s allowed to play the field. Unless you agreed to something where he would no longer use that site because of you. If not, I’d say it’s not necessarily reasonable to expect a call within one week, b/c imagine if you HAD to call back every person you met on the site and did a couple dates with. Maybe he just needs a little more time to devote to other people he met on the site, has a few options/things to explore, and thinks that you aren’t interested b/c you didn’t call . . .