The reward for information leading to Mollie Tibbetts is now over $400,000. Does the family pay that money to the person who gives the information? The local police department? Iowa taxpayers?
Generically, a specific person or group puts up the money. It could be the family but doesn’t have to be.
Government money is not a factor.
In this case I think the substantial majority is coming from donations. The initial reward offering was $2,000 (half from Crime Stoppers and half from a neighboring business) so I very much doubt that Crime Stoppers is putting up much money. The parents come across as middle class so there are limits on how much they can personally offer.
Actually it is Crime Stoppers operating the donation fund: