You hv to check when is your cut off day for payment in 新世界.
For example your cut off day in 新世界 is the 6 of every month.
If you transfer your mobile number to Smartone on the 4 of Aug. Then 新世界will not dedcuted one more month from your auto pay. But if you transfer after the 6 of Aug for example you transfer over on the 10 of Aug.
As新世界had already deducted the payment from your account on the Aug 6 for the period (Aug 6 to Sep 5). That means you have to pay double for the month of Aug one for 新世界 and of course Smartone will also charge you from the period from Aug 10 to Sep 9. That means you will pay extra for the period Aug 10 to Sep 9.