Translation:They spent the whole evening on a social network.
Alf42 is absolutely right and this was well-corrected. Longer version follows with some additional information for the curious about the oddities of preposition use here (prepositions being curious beasts at the best of times).
The original error was probably born of the other context in which someone can indeed be in a social network, as per the famous MySpace proclamation that:
"[absolutely anyone] is in your extended network".
But yes. While someone can be "in" a given network of people, be it social or professional, online or off... in this context, definitely "on", simply because of its use as a set phrase, after the fashion of, as you say "on Facebook, Twitter, etc".
The time marker is actually what makes the context clear here - one is hardly likely to be "in" a given network only for an evening, let alone talk about that period of time as "the whole evening", as though this is a long time. One is usually "in" a network of people for years - but "on" the site (in principle, lol) only briefly here and there.
I have been on Facebook ("a social network" - as a set phrase) a few times this morning / since 2008.
I have been in the associated groups of people (each being "a social network" - in the literal sense, but not in the sense of the set phrase) for many years.
Unfortunately, "social network" is not a term that I have generally encountered in this context. Common terms are "social media" for the general case and "social media platform" for the specific case (when comparing different instances, such as "which platform do you prefer?"). The term "social network" is generally used for particular sets of connected individuals, and in this case people are in social networks on social media platforms.
"Social networking service" and "social networking site" are term also used.
Neither option, in/on a social network, sounds good to me here. I think it's because "on Facebook" has become so used that I almost think it should be "on social network" even though that doesn't make grammatical sense. And if it was just network, you can be in a network or on the network. I agree with David that the time reference makes it a bit more understandable to use "on" but unless I had to use the exact phrase "social network" I would have specified which social network...Facebook or vKontake etc. I was on.