Warriors land 5 attacks quite often. And I almost never see six (and when I see, there is usually other reason to that). Your theory that each weapon just contrubutes it's four attack can be dropped at this point. Would be that the case, we would see six or more hits less often then 5 but reasonable amount of time. You can also see rounds where you produce only 1 hit, in your theory you would hit at least twice (first attack for a weapon don't fail).

If you watch fights you can see that weapons interleave during a round so it is not a simple: "one weapon delivers 1-4 hits, other weapon delives 1-4 hits".

So it MAY be something like this (this is only a version however):
primary weapon hits
secondary weapon checks for hit (probably starting straight from "second attack" skill chances (or first attack with reduced chances)
primary weapon checks for second attack
secondary weapon checks for second(third) attack
primary weapon checks for third attack
secondary weapon checks for third attack
etc
capped at 5 hits per round.