I dunno, does it say "units hit by", "when hit by", or "when wounded by"? These would all be slightly different.
And I'd think that the str 3 isn't the point.....it's to debuff it for the next salvo.
Your on to something,
Rad Shell 12" Str 3 Ap - Assault 1, Blast, Rad Charge
which to me says the Rad doesn't take effect unless there's a wound
Rad Charge: Every model in a unit
HIT by one or more rad shells suffers a -1 penalty to their toughness untill the end of the turn (this can affect the victims' instant death threshold)
this however makes it pretty clear cut that all you need to do is
HIT. Of course this doesn't really clear up the initial question of does the -1 toughness count for that initial salvo or just subsequent salvos that turn?
It still makes sense to me that the firing unit wouldn't benefit from the -1 toughness as it is all simultaneous but it needs an FAQ for sure