Hosting a party means you organize and foot the bill. If you invite people and expect input /contributions then you have to call it a potluck. Not being clear is totally inappropriate leaving people wondering and putting guests in an awkward position.
By the same token as a gracious guest to someone's house party, it's never inappropriate to bring a bottle of wine or flowers or whatever depending on the nature or ambience or whatever is suitable.
The good old standby solution is to pick up the phone and ask. I don't know why people shun this age old past time of communication. If someone is not clear about something, what is the harm in asking? Let's put it this way, if the host is upset or uncomfortable you asking them, then they shouldn't have put you in the awkward position in the first place. They should have been clear. So you know for next time if tables are turned that you know if you're hosting something, you can be clear so you don't put guests in the same position you are being put in.
Meanwhile back at the ranch- you weren't clear either- is Jane or John Host the birthday girl or boy? Or they are throwing a party in someone else's honor?
In the adult world, if I am hosting a birthday party to honor a friend of mine and I invite people to share that party, I would be clear that everyone chips in at a restaurant. Any party I've been to that's been hosted at a restaurant I've never not contributed my share. But I've never also had any confusion with the instructions and if anyone ever did invite me for somethikng and I wasn't clear, I just always ask for clarification, becuase that's just me, I like to communicate with people :) It's really easy. Give it a shot.
And in the mean time, bring enough money yo cover your share of the dinner. Unless it's Hugh Hefner throwing a party and you can expect the whole gig is covered, you should be respectful and bring along enough cash for your share of food and drinks and tip.