DAB uses OFDM modulation, which has a guard interval between each symbol transmitted, and the symbols have an accurately known repetition rate.
The receiver uses this plus to derive a clock that matches the transmitter plus the (mostly constant) propagation delay, then uses that timebase to produce the audio sample clocks.
For example mode 1 DAB has a symbol period of nominally 1ms, which the receiver will lock to then effectively PLL up to give a notionally 48KHz clock for the audio stage. There will be some buffering, inherent in the MP2 decode, but it will be constant length.
Note that the clocks at the receiver will in a moving receiver differ from the transmitter clocks due to doppler shift, but that does not matter because the symbol rate will differ by the same amount, thus data will still be available when it is needed.
Absolute time (To the extent that it exists) is an irrelevance, all that matters is that the LRClk frequency matches the appropriate multiple of the received symbol rate.
There are actually similar tricks used in some AOIP schemes where the ethernet packet rate drives a PLL to generate the audio clock.