When a form field is filled the fields value is populated and (optional) a visual appearance for the form field is generated reflecting the newly set value. So the reason that you are seeing the value when you click into the form field is that the fields value will be displayed but as long as the field is not activated the fields appearance is used.
If you tried setting the value with PDFBox 1.8 you might try using PDFBox 2.0 as this now has unicode support and the appearance generation is redone.
You also need to ensure that the font you are using in the form is available on the system you are filling your form with. Otherwise with PDFBox 2.0 you might get an error message similar to
Warning: Using fallback font 'TimesNewRomanPSMT' for 'MingLiU'
Exception in thread "main" java.lang.IllegalArgumentException: No glyph for U+5185 in font MingLiU
Which is as MingLiU is not available on the system it has been replaced by TimesNewRomanPSMT which doesn't have the character needed.
As another solution you can also direct the Adobe Reader to calculate the appearance for you when the form is opened using
PDAcroForm form = doc.getDocumentCatalog().getAcroForm();
form.setNeedAppearances(true);
again using PDFBox 2.0
I've created a little sample using PDFBox 2 but creating a form from scratch to test if it can handle the Chinese text
// create a new PDF document
PDDocument doc = new PDDocument();
PDPage page = new PDPage();
// add a new AcroForm and add that to the document
PDAcroForm form = new PDAcroForm(doc);
doc.getDocumentCatalog().setAcroForm(form);
// Add and set the resources and default appearance at the form level
PDFont font = PDType0Font.load(doc, new File("/Library/Fonts/Arial Unicode.ttf"));
PDResources res = new PDResources();
COSName fontName = res.add(font);
form.setDefaultResources(res);
String da = "/" + fontName.getName() + " 12 Tf 0 g";
form.setDefaultAppearance(da);
// add a page to the document
doc.addPage(page);
// add a form field to the form
PDTextField textBox = new PDTextField(form);
textBox.setPartialName("Chinese");
form.getFields().add(textBox);
// specify the annotation associated with the field
// and add it to the page
PDAnnotationWidget widget = textBox.getWidget();
PDRectangle rect = new PDRectangle(100f,300f,120f,350f);
widget.setRectangle(rect);
page.getAnnotations().add(widget);
// set the field value
textBox.setValue("木兰辞");
doc.save("ChineseOut.pdf");
which works fine. I also tested with the font you are using unfortunately this had an error as MingLiU is a TrueType collection which PDFBox can not handle at that point in time.