Among Singapore's entry requirements for visiting foreigners (accessed here) is:
Onward or return ticket (if applicable)
When is this requirement not applicable?
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Yes. In my experience they do. Or at least the airline which will get you there will require you to have an exit ticket in order to board.
I was traveling from Phuket to Singapore without an exit ticket from Singapore (although I had an exit ticket from Sydney 2 weeks after) and the airline wouldn't let me board without an exit ticket. It was a pain. In the end I ended buying a $40 ticket at the airport which I never used.
I know this answer lacks any specific information regarding actual regulations, I am just sharing my experience. Hope it helps.
EDIT: When I answered this question the title was "Does Singapore require all tourists to present proof of onward travel?"