Hi Mike,
I doubt it's been done (it's not even a feature of the tagit library), but looks to be a trivial change.
I think it's here in the source code, and you'd change it from:
if (e.toLowerCase().indexOf(tag) == 0) {
to:
if (e.toLowerCase().includes(tag)) {
EDIT: just confirmed that this works. Would be awesome to add it as an option in the widget.