It is actually the Adelaide Destitute Asylum not Adelaide Detention Asylum.
This link may be helpful.
Register of admissions to the Destitute Asylum, Adelaide (1870 - 1924)
http://www.findandconnect.gov.au/sa/biogs/SE00547b.htmIt says
Details of persons (including children) admitted to the Asylum. Among other information entries provide name, age, nationality, religion, relatives, admission and discharge details and where discharged to. Notes on contents - A card index to this series is available. Each card gives (1) Name, (2) Age, (3) Residence, (4) Number of children, (5) How long in colony, (6) Ship, (7) Trade, (

Year of application, (9) Page of entry or entry number, (10) Nationality. Date range - 1870-1873, 1881-1924.