I did give the confinement lady (from Hell) a red packet of $20 when she starts work and after she completed the work, I gave her another red packet of $20 with a box of baby full month's cake.
There is no rules how much we have to give them since they will be paid. The amount in the red packet is purely for good luck and yes, as part of the chinese custom only.
If you like the service provided by your confinement lady, you may consider giving her a slightly bigger red packet. For me, she was not as good as she said and turned out my mum did most of the job than the confinement lady.