Not necessarily. It depends on what materials the thing is made of. For example, any cobalt in the structure will be activated to cobalt-60 half life 5+ years, and carbon will get activated to C-14 half life of 5760 years. Then there is neutron embrittlement of any steel structure.
What isotopes were you referring to?
1) a fusion reaction simply produces fewer neutron emissions per amount of energy released (which stands to reason since the fission process is itself driven by neutron emissions and produces more of them).
2) less energetic neutrons are emitted (more of the fusion reaction release of energy is in the light spectrum), which should produce fewer transmutations in the surrounding materials;
3) a proportionately higher percentage of the transmutations that do occur create isotopes with shorter half-lives (I believe this follows from #2).
4) There are differences in the blanketing material: fission reactors (as someone pointed out) use stainless steel as the containment vessel and this is subjected to heavy neutron bombardment. Most of the fusion deesigns I've see seem to be using copper jackets as a blanketing material/heat sink. So the transmutations that occur will be different than the ones in stainless steel.
But I'm not sure a 100% about any of this: I'm just cobbling together what I can remember from the articles I've read on possible fusion reactors.
As a side note, one of the big issues with fusion reactors is that the neutron bombardment of the superconducting magnets transfers heat and/or destroys the crystalline structure required for superconductivity (although I think the higher temp superconducting materials are more resistant). I believe the Lockheed design addresses this in part because the containment envelope is designed to recapture more of its own neutron emissions, in effect partly converting the neutron emissions into more deuterium and tritium fuel. Really clever.