If I turn on data roaming, won't they charge me a lot of money
through the overseas telecom company?
I read horror stories of people racking up thousands of dollars
of bill when they go overseas and use their phones to surf net.
Damn scary. 
Of course they would. So far, singtel standard rates is 22
dollars per mb. Smartphones have the option to disable overseas
data roaming, found in the network settings.
So far I have used the data roaming in japan, thailand, and
vietnam, but on singtel's packaged day/s rates, and I love it. If
you researched, its actually cheaper than to get a local sim card.
I get unlimited data for the number of days paid for. Cheapest I
got was $15 per day to $100 for 5 days.
Most important thing to note is that the rate is only applicable
to singtel affiliated network, so must use manual network selection
to lock that network, otherwise a whole new set of charges apply,
than yes you see hell on your bill.