Nicolejoy, this used to be the case but the Singapore laws on DHs have changed recently. It is now mandatory for Singapore employers to give their helpers one day off for those starting on fresh contracts. However it is not mandatory to give the helper the gazetted public holidays off. The market rate for pay in Singapore is also now higher - not as high as HK but due to the strong SGD makes the salary about on par. As far as I know most families who bring their helpers along from HK do not pay the Singapore rate, but retain the HK level of salary, meaning that the 'transfer' helper is earning a good deal more than their counterparts in Singapore, due to their experience and good relationship with their employer. I have had friends who have brought their helpers over from HK to Singapore and it is purely a matter of agreement between both parties. In the case of one family who had 2 helpers, one helper chose to move with the family to Singapore whilst the other preferred to remain in HK.
Ives, there are plenty of Singapore agencies that handle transfer maids from HK. It is also to handle the paperwork yourself with the Ministry of Manpower.