You are right in saying that the word infective does not fit in the sentence "His enthusiasm was infectious."
NOAD says: "[...] infectious usually refers to the spread of positive things, such as good humor or optimism."
In this light, we should use the 'rule' exemplified by NOAD, as you said. So, in figurative sense we should say "His enthusiasm was infectious", not "His enthusiasm was infective." (See the NGRAM below.)
In order to answer your second question, first of all we should note that it is not true that "when talking about diseases, both the words seem to fit." In fact, as we can read in Merriam-Webster's Medical Dictionary, "infectious disease" is defined:
a disease caused by the entrance into the body of organisms which grow
and multiply there;
while infective is defined:
producing or capable of producing infection.
In this light, it seems that infectious is referred to the process, while infective is referred to the agent.
However, for instance, we can usually speak of "infectious hepatitis", but not of "infective hepatitis" as OAD defines this usage "SPECIAL USAGE - DATED".
The following NGRAM describes 'enthusiasm was infectious', 'enthusiasm was infective', 'enthusiasm was contagious'.
Also, "enthusiasm was infectious" ("enthusiasm was contagious") gets 38,900 (50,200) hits on Google Books, while "enthusiasm was infective" gets 5 hits.
In the Ngram I also reported "enthusiasm was contagious" because in non-technical texts there is little or no distinction between infectious and contagious.