Sometimes fuses are needed, because they have the potential to clear a bigger fault faster than a corresponding breaker.
However, many times, an electrician installs a fused disconnect because it was just easier to source than a non-fused disconnect.
I agree with MixManSC that having the breaker trip first is safer, as it should interrupt all three phases together.
Anyway, what you have is a "coordination" issue. You burned out a fuse before the breaker tripped, when what you may really want is to trip the breaker first.
If that is the case, you might want to replace those fuses with time-delay fuses at 30A.
OR, if you know for sure that fuses are not required in this disconnect (an electrician can verify this), then there is such a thing as a "dummy" fuse that you could use that would never blow, which would convert your fused disconnect to a non-fused one. Sometimes when an electrician installs a fused disconnect, they just put in fuses, because they need to stick something in there.