A report found children at St Ninian’s Residential Care Home were targeted with sexual and physical abuse.
The £10,000 payouts have been given to those who were abused in care before 2004, with more than £4m spent.
Up to £9m will be awarded to the Future Pathways group, which provides therapy and training to survivors.
Reassurances have been offered to those who may wish to take part in the inquiry.
Lady Smith’s call for evidence comes ahead of the Phase 6 case study, which begins this summer.
Findings published after third phase of the Scottish Child Abuse Inquiry.
The Labour-led Scottish Executive felt an inquiry 'was not the best way to proceed'.