Class-level spec https://docs.oracle.com/en/java/javase/14/docs/api/java.base/java/io/PrintStream.html#writeBytes(byte%5B%5D) as well as specification for various writeX methods have the following assertions:

"a PrintStream can be created so as to flush automatically; this means that the flush method is automatically invoked after a byte array is written"
"If automatic flushing is enabled then the flush method will be invoked"

It looks like PrintStream::flush is expected to be called, however the OpenJDK implementation calls ::flush method directly on the wrapped OutputStream.

Consider the following code:

        new PrintStream(new OutputStream() {
            @Override
            public void write(int b) throws IOException {
                System.out.println("OutputStream::write");
            }
            @Override
            public void flush() throws IOException {
                System.out.println("OutputStream::flush");
            }
        }, /*autoFlush:*/ true) {
                @Override
                public void flush() {
                    System.out.println("PrintStream::flush");
                    super.flush();
                }
        }.write(new byte[]{0, 1, 2});

For OpenJDK the output would be:

OutputStream::write
OutputStream::write
OutputStream::write
OutputStream::flush