The creator seems to be referring to flare stars. Flares may be magnetic in origin, like various manifestations of the Sun's magnetic field. These flares can be quit luminous across the electromagnetic spectrum, including in the x-ray wavelengths.
Some red dwarfs are flare stars, though flare activity may be largely restricted to a small part of a red dwarf's lifetime. However, during this period, life on a planet orbiting close to a red dwarf could be in serious danger.
The reference to convection may be that red dwarfs are generally fully convective, unlike other stars. Magnetic fields in stars are generated via the dynamo effect; in red dwarfs, full convectivity can play a huge role in generating strong magnetic fields, and thus stellar flares.
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