Recieved offer from City on PgDip Nursing but panicing

I will greatly appreciate any help on this or guidance.

Having received a conditional offer from City today subject to 'satisfactory' DBS clearance, reference clearance and an APL pass,

I am terribly worried over the DBS clearance, I declared on my UCAS application that I do have a 'caution' and I was going to explain this caution during the selection day however the lady who escorted me into the interview room told me not to worry of this as it's not important till placements. Hence on the day, I never discussed my DBS but now they have put DBS clearance as a condition I'm afraid I won't be accepted. Having enquired with admissions, they've told me they'll tally the DBS with the UCAS application and invite me to explain whats on there in front of a panel but she didn't sound too sure, can anyone tell me who has been in this position what the case will be? Thanks