It can be complicated.
I did not include a Singapore PCC at the time of AOR, because presumably it could be done only with a request sent by the IRCC after they had started review the application.
Then I tried to get it using the ITA. It worked and I submitted it via CSE.
A week after that I left Singapore and moved to Canada, and got an ADR requesting a Singapore PCC. I re-submitted the PCC that I had already sent via CSE.
A week or two after that, I got a message that my CSE had been processed and the document that I had uploaded (i.e. the Singapore PCC) had been added to my profile.
So what happened was that IRCC received my Singapore PCC when I was still in Singapore, but had not added it to my profile before they sent me the ADR for the same Singapore PCC, by which time I had already moved to Canada.
I guess one could argue both ways whether I need to get a new PCC from Singapore. I've decided not to pay the extra money to get a new one. The worst-case scenario is that my application gets rejected and I'll just apply again.