The primary action (little balls) is not a melee attack.
The secondary action (lightning) is not a melee attack.
The weapon special is a melee attack, but does not have a primary or secondary action.
Test show that the crit chance bonus is applied to the primary and secondary action.
The word “melee” is wrongly placed in the description.
I did more testing. It seems like it was incredibly bad crit rng in my earlier tests.
Staffs with 80% crit bonus and:
no blessing
warp flurry
warp nexus
warp flurry and warp nexus
all show the expected crit rate for the assumption that the “primary/secondary action melee critical chance” really is additive “primary/secondary action critical chance”.
I edited the OP and moved it to the bug report section, for the description falsely containing the word “melee”.