setTimeout for the win. Thanks, Dojo!

TimeTextBox.js

// setTimeout() because the keystroke hasn't yet appeared in the <input>,
// so the get('displayedValue') call below won't give the result we want.
setTimeout(dojo.hitch(this, function(){
  // set this.filterString to the filter to apply to the drop down list;
  // it will be used in openDropDown()
  var val = this.get('displayedValue');
  this.filterString = (val && !this.parse(val, this.constraints)) ? val.toLowerCase() : "";

  // close the drop down and reopen it, in order to filter the items shown in the list
  // and also since the drop down may need to be repositioned if the number of list items has changed
  // and it's being displayed above the <input>
  if(this._opened){
    this.closeDropDown();
  }
  this.openDropDown();
}), 0);