Generally, this signal is enough to handle a completion selection and it just used to complete the entry according to the selected completion string.

 final DataColumnString column;
 final EntryCompletion completion;
 
 completion.connect(new EntryCompletion.MatchSelected() {
     final String text;
     final Entry entry;
 
     entry = source.getEntry();
     text = model.getValue(iter, column);
 
     entry.setText(text);
     ...
 });