I believe the tritium issue is addressed through the inclusion of lithium in the reactor's inner blanket [1]. Something about the neutron interaction with the lithium results in some non-trivial production of tritium which is then freed into the reactor. tl;dr - they've thought of that.
Isn't this the case with nearly every aspect of "proposed" fusion reactors. Just because it's proposed or "not yet tested on a commercial fusion reactor" does not necessarily mean that the mechanism is not well understood.
I think if it were so well understood, ITER wouldn't be testing over 100 different breeder blanket designs. I've seen breeder blanket design described as one of the biggest challenges with fusion today.
I would expect that it is more a matter of selecting the best/optimized design rather than demonstrating the fundamental viability of tritium breeding.
[1] https://en.wikipedia.org/wiki/Breeding_blanket