To summarize the current rule:
1. No one is charged for just parking during the day at a Disney resort, e.g., if going to a resort for a dinner reservation, you will not be charged for parking while there; the fee applies to overnight stays.
2. A DVC member who reserves a room at a DVC resort either for points or cash will not be charged for parking during the stay. The member also will not be charged for parking at a non-DVC Disney resort at WDW if the member uses the membership and points to make the reservation; the member will be charged for overnight parking if the member has a cash reservation at a non-DVC Disney Resort.
3. Any non-DVC member who has a reservation at a DVC resort, which reservation was made by a member using membership points, e.g., such as a DVC member reserving a room for relatives or renting a reservation using his points, does not pay for parking at the resort.
4. As noted in the post above, mistakes can be made at the resort and someone can be charged for overnight parking despite that there should be no charge. Thus, it is best to check any charges made to you at the resort before you check-out to assure you have not been charged for parking, so it can be corrected before you leave.
5. As to actual price of overnight parking, the value resorts are $15 per night, moderates $20, and deluxe (including all DVC resorts) $25, see
https://disneyworld.disney.go.com/guest-services/parking/