My interpretation of the graph is that Singapore did too good a job in the early part of the spread.
The strategy did not take into account the fact that the majority of cases were asymptomatic as this crucial fact wasn't known at the time. It was assumed that 80% of cases were mild and 20% would require various degrees of treatment and that was it.
As more data has come to light we now know that while all this aggressive contact tracing was going on there were literally thousands out there who were completely symptom free but were spreading the bug.
What we are now seeing are cases that caught the virus from this asymptomatic pool and have ended up sick enough to seek treatment.
The end result has been a delay in the flattening of the curve. You can clearly see the kink in the middle of the log graph as the result of the aggressive earlier containment measures but the asymptomatic cases burst the bubble resulting in an increased rate of transmission around mid March.
My estimates are that there are anywhere between 50,000 to 200,000 who either have the virus or it has come and gone without them knowing.
That is why a random sample which includes antibody testing is crucial in order to get a true picture of situation. Without this data everyone is trying to fight the virus blindfolded.