Backing pub name — on reflection like the Oracle (9)
I believe the answer is:
prophetic
'like the oracle' is the definition.
(oracle can mean a prophet or seer)
'backing pub name on reflection' is the wordplay.
'backing' becomes 'pro' (being pro something is backing or supporting it).
'pub' becomes 'ph' (abbreviation).
'name' becomes 'cite' (I've seen this in other clues).
'on reflection' is a reversal indicator.
'cite' in reverse letter order is 'etic'.
'pro'+'ph'+'etic'='PROPHETIC'
(Other definitions for prophetic that I've seen before include "Divinatory, prescient" , "Forecasting" , "Foreseeing future events" , "Foretelling events" , "Oracular, predicting events" .)