The modelling drove her decision to enter a hard lockdown and "supercharge" contact tracing efforts, she said.
While the lockdown was downgraded on the weekend after contact tracers realised an infected worker had not come into contact with as many people as claimed, Ms Spurrier maintained she made the right call.
The commissioner said although the employee's actions had an "unbelievable impact" on South Australians, there was no penalty for lying and he won't be charged or fined.
The premier added he was proud of every single South Australian.
However, community sport and recreation centres are still not allowed to operate.
South Australians are urged to wear masks where they can not physically distance.
South Australia recorded just one new case on Sunday, a woman in her 20s who is quarantined in a hotel after travelling overseas.
There were no new diagnoses in the Parafield cluster in suburban Adelaide, which remained at 26 cases.
Though Prof Spurrier admitted due to there only being a small number of cases, there is a "great degree of uncertainty" with the modelling, though it was absolute SA was facing a second wave.
"We are not out of the woods yet", he said, warning there would be positive cases in the days and weeks ahead. On Saturday, there were only around 93 cases active throughout the country.
Almost 17,000 tests were carried out on Saturday.
"I know this has been a very challenging time for the people of South Australia, but we have avoided a catastrophic situation in our state by following the unequivocal advice", Mr Marshall said. Police seized electronic devices from the worker.
The worker is believed to be a 36-year-old Spaniard living in Australia on a temporary graduate visa.
Police will provide a comprehensive briefing on the investigation into the pizza shop on Monday, Mr Marshall said.
People in Australia must stay at least 1.5 metres away from others.