There is a phenomenon known as a moreton wave, which is analogous to a 'solar tsunami'. It occurs on the surface of the sun, and is essentially a shock-wave created by large explosions on the sun (such as a solar flare). They do not leave the surface of the sun, and occur frequently, with no consequences for us.
The 'solar tsunami' shown in the Doctor Who episode is fiction, and is rather like the 'killshot' solar flare depicted in the movie 'Knowing'. It has no relationship to reality.
By the way, I think that the current 2-part episode depicts the formation of the 'Nestine'. What do you think?