There are two main causes for the difference in timing between analogue and digital radio and TV signals.
The main cause, which is true of all digital transmissions, is that digital signals are all encoded in some way, so the transmitter has to encode the signal for broadcast and the receiver has to decode the received signal before playing it to you.
You can actually see this effect in action if you have an analogue radio, a cheap DAB radio and a more expensive DAB radio all tuned to the same station.
The analogue radio will play the signal first, then the more expensive DAB set, then the cheaper DAB set. The difference in DAB sets is due to better sets having faster processors that decode the signal faster.
The second only applies if you are getting the digital signal from a satellite, in that case the difference is caused by the longer path of the signal travelling up to a satellite in geo-stationary orbit then back to Earth. This is the cause of the 'satellite lag' you sometimes see in live news broadcasts where the two locations are linked via satellite feeds.