It's a bit hard to say without seeing some code, but importing just sets a reference, exactly as with variable assignment: that is, if the data changes, the references change too. Naturally though this only works if it's the parent context that you've imported (otherwise assignment will change the reference, rather than updating the value.)
In other words, if you do this:
from mypackage import mymodule
do_something_with(mymodule.MY_CONSTANT)
#elsewhere
mymodule.MY_CONSTANT = 'new_value'
then all references to mymodule.MY_CONSTANT will get the new value. But if you did this:
from mypackage.mymodule import MY_CONSTANT
# elsewhere
mymodule.MY_CONSTANT = 'new_value'
the original reference won't get the new value, because you've rebound MY_CONSTANT to something else but the first reference is still pointing at the old value.