The neutrons released by the fusion reaction can be captured by the atomic nuclei of other materials it encounters, in a sense fusion. This induces radioactivity in those materials, called neutron activation, but won't create a run-away reaction. Nuclear fission reactors also produce neutron radiation that behaves in the same way, except in nuclear fission fuel it does create a chain reaction.

> Sounds a bit like a nuclear reactor.

They are nuclear reactors. Nuclear fusion reactors, rather than nuclear fission reactors.