Yes, as others said, Traits on weapons should only trigger on that particular weapon, but the effects apply to all attacks (unless the description says otherwise, but I don’t think any of them do) . But there has been a (usually minor) exploit, at least in VT1, that makes things wonky. You used to (and possibly still do) activate the effect on the weapon you have out when an attack hits, not the one that made the attack. This means that with certain weapons, you could shoot a far-away enemy, quickly switch to melee, and then trigger the melee weapon ability on ranged hit. This or something like it may have been at work here. It may also have had something to do with synchro issues (i. e. lag).
Btw, I seem to be typoing like crazy today. Its annoying, and I wanted to complain. Please ignore and continue.