Create the array by calling split() on the string:
var visList = '1234,5678,9'
var visListArray = visList.split(",");
You cannot substitue a string that looks like code for actual code. While this would work:
var visListArray = new Array(1234,5678,9);
Yours doesn't because the string is not interpreted by the Array constructor as 3 comma separated arguments, it is interpreted as one string.
Edit: Note that calling split() on a string results in an Array of strings. If you want an Array of numbers, you'll need to iterate the Array converting each string to a number. One convenient way to do that is to use the map() method:
visListArray = visList.split(",").map(function (item) {
return +item;
});
See the compatibility note for using map() in older browsers.