They do not need to check in together, however they do need to be listed on the reservation. They will not let someone, whose name is not listed on a reservation, check in for the party.
The first person to check in can do so for the entire group, getting everyone's keys, etc. Then the later arrivals can just meet up with the early arrivals when they get there. Or the early arrivals can get only the keys they need, leaving the others at the front desk for the later arrivals.
Also, if you have the dining plan it needs to be paid for at check in. I'm not sure if each part of the group could pay for their own dining plan or not. If not, the first person to check in would be expected to pay for the entire plan.