Coincidentally, I have just had a conversation with a chap at the DVLA about this very thing. As it stands, the first licence fee is a one time fee only paid upon registration. So when you buy a nearly-new car as a second keeper, the tax due upon purchase will be the standard rate for that vehicle whenever that is (even the day after registration), in your case CJ, £280 as it went up on 1 April.
The seller will get a refund for unexpired tax based upon the standard rate, not on the first licence fee. So they will get an amount equal to £270 divided by however many full months are left. (Not £500 divided by...)
However, under the new system introduced on 1 April, there is a bit of a fly in the ointment that the man in Swansea was unable to clarify:
The new First Licence rates for some cars (those with CO2 of 100g/km or less) is less than the new Standard Rate (£140), so any refund due in year one, if calculated the same way, could mean a refund of more than the First Licence rate paid, which obviously isn't going to happen. But he didn't know what would happen. So that's still open for discussion in Swansea.