There was an answer, now deleted, regarding the energy resulted from the annihilation of a proton with a anti-proton and the comparison with the energy resulted from fusion. Too bad it was deleted, because there are conditions in which the answer was valid.
In the event of matter/anti-matter annihilation, the energy is likely to be emitted in any direction. And it's many orders of magnitude higher than the chemical bond energy.
Which means a gamma emitted towards the planet is very likely to vaporize some anti-matter and eject it in space towards the cloud of matter above. Would this anti-matter be electrically charged (very likely at the level of energy we are speaking), the magnetic fields will deviate the ejected antimatter in areas where the cloud wasn't repulsed by the "initial" explosion.
With enough density of normal matter in the cloud, you may assist to a cascade effect causing a gamma storm engulfing the entire surface of the planet.
Which bring us to the important parameters which describe what happens on the anti-matter planet - the (absolute) density and the distribution thereof for the matter cloud.
- On one extreme - if is homogeneous and zero, nothing happens.
- On the other extreme - if it's homogeneous and dense enough, you may see a gamma storm which cause the entire planet to be evaporated and thrown into space as an ionized plasma of antimatter.
In between, various other scenarios - regular pulses being improbable, though not impossible - e.g. still happen if the "cloud" is instead a "galactic stream of cosmic dust - after repulsing a "wave" by a gamma burst, the stream renews the density of the cloud with other incoming matter.
See also: Herbig-Haro objects - protostars for which the accretion disk falling into the forming stars ionizes and the created magnetic field ejects polar jets at "supersonic" speeds. Those jets collide with the surrounding nebula and produces EM emission in visible spectrum (recombination and bow shocks) without the corresponding (for a mature star) IR part of the spectrum.
How's the above relevant? Well, astrophysical magnetohydrodynamics is complex enough to allow a pulsating phenomenon (caused by the described configuration) to actually occur in the right conditions.
It is also conveniently complex enough to allow for quite a fair bit of plausible hand-waving; feel free to do it I don't think someone will jump to say: "No, that's impossible", especially after accepting the presence of an anti-matter planet.
To asses the safety of handwaving, a google search for "pulsating bow shock" brings in something like:
... The process is complicated by the existence of a whole class of pulsating shocks for which no macroscopic theory has been fully developed
Approaching the shock the density of diffuse super-thermal ions increases about exponentially causing the interaction to readily become non-linear, causing the pulsation wave amplitude to grow and steepen during the downstream connection towards the shock ramp.