It depends on what you mean by "author of sin." Obviously, Calvin used the language to describe God's involvement (see quotes above) but the Westminster Confession explicitly denies that God is the author of sin. So who is right? I believe that people equivicate on the term "author." While the Westminster divines used the term "author" to describe one who commits sin, Calvin most likely used the term in a more 1st causal sense (i.e. decreed, predestined) than a responsible 2nd causal sense. I prefer the Westminster language simply because it is confessional and it is semantical to argue against it if one is simply equivicating.
Its clear Calvin is using the word "author" non-technically, not in the sense of direct or immediate efficient source and cause of the sin. In the closing section, he sums by saying:
So that in a wonderful and ineffable manner nothing is done without God's will, not even that which is against his will. For it would not be done if he did not permit it; yet he does not unwillingly permit it, but willingly; nor would he, being good, allow evil to be done, unless being also almighty he could make good even out of evil. 1,18.3.
When Clark and the WCF use the word author, they mean it in its technical sense of direct immediate efficient cause.
And I bet right there Calvin has calamity in mind, hence his reference to Job.
Take care,
David