The planet's journey to clean energy use has taken another leap forward in Naka, Japan, where the world's biggest and most advanced experimental nuclear fusion reactor has...
Deuterium tritium fusion releases helium-4 and a fast neutron. So most fusion schemes will involve producing radiation. However, the fuel can't keep reacting without carefully controlled conditions so there is no meltdown risk or runaway reaction scenario. Vessel components may be activated by neutron bombardment and will still require careful handling when servicing the reactor.
There are aneutronic fusion reactions, but they require higher energies and face problems with sourcing the fuel. For example helion energy plans to use Helium-3 with deuterium. Although even their fuel cycle won't be completely aneutronic.
Fusion is far safer than fission, but let's not spread misinformation.
The fuel itself won't stay radioactive as you point out. There is however neutron radiation produced while the reactor is running. This necessitates shielding for components and personnel.
Additionally there's a phenomenon called neutron activation, where a non-radioactive substance absorbs neutrons and becomes a slighter heavier isotope that is radioactive. For something like a research vessel with relatively little operation time and low fluxes, this isn't a major concern. For power generating reactors with high flux over long periods of time, this will make some reactor components radioactive. That means servicing and decommissioning fusion reactors will still require protocols to monitor and control contamination.
Since there's no risk of meltdown, none of this poses a risk to the general public. So fusion is indeed much safer than fission, but you can't just say there's 100% no radiation. That is erroneous.
An x-ray machine doesn't stay radioactive when not in use, but it still produces ionizing radiation when it's on. Fusion power is similar. The radiation produced mostly goes away instantly, but is definitely present during operation.