Did you have a provisional licence before? You should not have to go back to provisional status for drink driving - unless the court ordered you to retake your test?
if you were in the high risk category (blew 88 or above, second conviction in 10 years or failed to supply) then you ARE required to submit to a medical before you get your licence back and this is a DVLA administrative mess up.
i expect it is tempting to take the licence at face value, but the problem will come at some point in the future when they realise their mistake and then require you to undertake the medical. This could be when you apply for your full licence, or indeed after that when you seek to renew it in 10 years time. They can still invoke the requirement for a medical.
at present, because you were banned before 1st June 2013, if you point out the need for a medical, you will be able to ask to be allowed to drive under s88 Road Traffic Act 1988 if the process stretches on beyond 7/9/15. This loophole has now been closed and it will probably mean that when at some point in the future they realise their mistake and then revoke your licence, you will not be able to use this loophole and will remain without a licence for weeks while you wait for the results.
Where are you at currently with alcohol consumption?