Ideally, if your humidifier is properly sized for your humidor and you keep it charged then you should have no need for additional humidification except in winter months when the heater is blasting. At those times you should augment your regular humidification with an additional source. However, distilled water is not somethign I would ever recommend because its a one way device, meaning it will never reabsorb humidity only release it.

If you are talking about a desktop humidor I highly recommend crystal gel humidifiers. They work better than anything else I have seen. A small crystal gel puck or drymistat tube in winter should help keep things where they are supposed to be.