Does kamma bind or work with the physical realm? Such as a tsunami will kill you, but you will also die in such a way due to past kamma?
Previous & current kamma can only effect(bind) if mind is impure. It doesn't mean that such kammas are of no effect rather these form a certain pattern which generates sankharas at subconscious state. If Ignorance still remains, clinging affect is generated due to sankharas, if not then there is no clinging affect.
This is the reason why arhants don't get disturbed by previous kamma ,cause they have no ignorance left(as only full awareness) hence sankharas cannot affect their mind rather their subconscious mind starts cleaning itself by 'letting go & to never let them come back'.
Regarding punishment through nature , if Arhant has made a commitment to do something , no nature or power can stop ,otherwise ,Arhants always remain ready to give-off their body to remove all suffering a.s.a.p. ... Still whatever the punishment is given to such Noble ones , that doesn't let their mind fickle by even a single bit. They remain at peace. That's why , effect of kamma within body remains to the degree/amount of Ignorance present.