Just reached home and tried the GPS again with "Faster Time" setting. The planned route is still asking to exit Tiong Bahru and go via Chin Swee Road to Riverside Point.
Tried using MapSource again on 091109 map, same result.
Not sure if you will also have the same suggested route. Origin can be anywhere before the CTE Tiong Bahru exit and destination is Riverside Point.
Since already traveling on CTE, would expect the route to continue on CTE and exit on Clamenceau Road / Merchant Road. Unless of course it's faster to travel on Chin Swee Road, which I assume is not the case.
I simulated this route from AYE to Riverside Point on my Nuvi and there was no problem. I suspect you may have another map that is interfering with this routing. What device are you using and what maps are installed? I have encountered such problems before on some other maps.