First of all, they are trying to be clever. At a dinner party, you serve up food so the writer is saying 'served up drama', which isn't really a phrase, in order to make the article more entertaining. So, to understand the phrase, think about them serving food. Instead of food, their guests got DRAMA. Drama from the hosts, served up like food. Presumably because "Beyonce and Jay Z barely spoke two words to each other the entire evening". Which people would see as intriguing or interesting or .... dramatic. That's all. It isn't particularly negative, no. EDIT: These sorts of magazines and articles love to talk this way. They fill them up with little made-up or invented phrases and wordplay in order to make stories that aren't interesting more fun to read.

Yes, context is definitely helpful here - was it from an entertainment article, by chance? It sounds like something an entertainment writer would use to get extra attention for an article. It's probably a play on chefs serving up a certain special dish at restaurant events. Someone (probably a celebrity) was "serving up" complications or revealing personal issues at a public event. Can't say for sure, but it doesn't sound like an expression native speakers would use regularly.

It might help to see the phrase in context, but more than likely it means to make things difficult, or more complicated than they need to be, which has a negative connotation.