Hi Ophelie,
The birth-death model assumes all tips are sampled at the same time. If you specify dates tips, BEAUti will warn you that this assumption is broken. BEAST will still be able to run the XML with this model and dated tips, but you cannot rely on it being a birth-death process.
If you have dated tips, you should use a birth-death-sampling model, like BDSKY, which does properly take the tip sampling process in account. Alternatively, coalescent models can handle dated tips, but in this case may be less appropriate for your data.
Cheers,
Remco