iOS 8.3 visual voicemail -receiving hours after call

May need to restart your phone or contact your cellular provider.

as stated talk to your carrier, the voice mail system is not an apple thing it's the carrier most of us around the world have no visual voice mail system

heck if I could I would remove my normal voice mail setup it's a serious pain from a long lost time

Do you turn off cellular data? Visual Voicemail requires cellular data to work correctly. If it has not been off it is a carrier issue, as already stated.