If you have the same station playing on two radios, one analogue and one DAB, you will notice there is a delay of a few seconds between the two. In fact, you will hear the DAB broadcast slightly after the analogue version.
There’s nothing wrong with your radio. If you have digital TV, you’ll find the same thing happens when you switch between analogue and digital transmissions of the same channel.
The techy answer is when the station originates as an analogue broadcast, the signal must be transformed into a digital transmission using MPEG2 encoding and COFDM modulation. This takes a couple of seconds, hence the delay when you hear it come out the other end.