My parents are from Singapore. Most of my father’s family still live there. We’ve just returned from a visit, where there was a large family event, attended by 50 plus people.
We’ve been maybe once a decade, so it isn’t a case of my being used to it, and not realising.
There is a difference between the Singaporean accent and Singlish. The family all have an accent but in day to day speech, talk with normal sentence construction. They can all talk Singlish and really ham it up by choice, but they don’t in normal conversations. People I interacted with in shops, the MRT and hawker centres also did not speak to me in Singlish. The children who my little girl played with in the play areas/splash parks of the tourist attractions also spoke properly - accented, but in normal sentences.
Even if he did pick up the accent, he will be likely to lose it. My brothers grew up in Singapore, and moved here at age 10 and 12. They both have a plummier RP than me. One went to private school, and the other just went to the local South London comp.
A few of my daughter’s friends happen to be from families who were ex-pat in Singapore for a period. (found this out when chatting about Easter plans, and we said we were going). All sound British now. The one that we knew from the point they relocated home, sounded American when she first got here. Same as my two cousins who went to international school in Indonesia.