OK, quite confusing. I assume you generate the pressure wave with the heating of the material, then there is no need to apply a second source of wave generation (say a force or pressure).
As I said it is important to know the material you have because as I said solid material support two different waves (pressure and shear).
Second of all what is exciting the wave - is the temperature or another form (say a force). With the temp. it should be possible like you have for instance laser excited ultrasonic waves in solids (due to rapid heating at the laser spot, the heat generated results in a wave in a metal say). So make sure the temp. increase is a transient, resulting in a transient force on the material and that might generate the wave.
Finally to capture the wave it depends how long (in time/sec.) the pulse wave is - say it lasts ~ 1 microsecond, then dt (time step) in the transient analysis needs to be one tenth of that so 0.1 microsec or less (this is just an example you know the time duration of your pulse, so use that). That will make sure that at least ten sampling points are used to capture the pulse.In the paper you mention, they have duration of ns, so you need to have something like 0.1 ns then - in your simulation the heating lasts for a second! Make sure you understand how they heat up the tumour and the timescales which are really small -Peter pointed this out to you.
So dt in thermal is one thing, but in transient structural we need to have enough time sample points to capture the pulse.
That is for the time steps. Spatially now:
Also we need to have enough elements to capture the physical extent of the pulse, so with the spatial dimension of the pulse (call it wave length), we need to have wave_length/8, element size.
See this paper for some details.
All the best of luck - that is it from me