Strictly speaking that's correct. However, if you bought your place in , for example, February, the seller is unlikely to be too keen to pay for this year's contribution, and since the bill generally isn't issued until June or so, it's a common dilemna. You could just stick to your guns and say you're not paying this year's because it's not your bill.
BUT, unpaid rates bills go with the property. So, when (if) you come to sell, and you go to the rates office to get the certificate stating there are no unpaid debts on the property, you may get a nasty surprise. Not only the outstanding year's payment, but interest and fines on top. if the debt is more than (5?) years old, it may be written off, but I'm not sure of the law on this. So be careful. On new builds, the developer
ought to pay the first year's rates, unless you signed on January 1st of course. If they don't, and you don't, you run the possible risk of the above scenario. For the sake of a couple of hundred quid, I paid ours (or rather, the developer's), my neighbour stubbonly refused to. Only time will tell who got it right.