The famous philatelist A. F. Bassett Hull explains O.S. as 'On Service' in his 1911 work 'The Postage Stamps, Envelopes, Wrappers, Post Cards and Telegraph Stamps of New South Wales'.
He does so with good reason.
From official Sydney GPO regulations, 1890:
the following is found near the end of the regulations:
Then in 1895 from Joseph Cook of Sydney GPO:
The confusion may arise because O.S. (On Service) is used on official stamps and envelopes.
A good way to remember the correct meaning is to recall O.H.M.S (On His/Her Majesty's Service) without the H.M. in between.