The reason for the difference between JavaScript and wolframalpha website is that JavaScript is calculating the years mathematically, so it includes the year zero. Try to set the year to zero in JavaScript and you will see that it works. However, there is no such a thing as year zero, and the year before year 1 is year 1 BC. Try to set the year to zero on wolframalpha website and you get an error, while it automatically converts all negative years to years BC. This is the correct behavior.
To get the BC years in JavaScript, add 1 to every year below 1. So year 0 becomes 1BC, and year -125 becomes 126BC. In JavaScript this gives you Sunday, and 126BC on wolframalpha website gives you Sunday too. 125BC gives you Tuesday on wolframalpha website, and -124 gives you the same in JavaScript.
var date = new Date();
date.setFullYear(-124);
date.setMonth(9);
date.setDate(31);
console.log(date.toString());
date.setFullYear(-125);
console.log(date.toString());