Dunno much about Arduino, but it seems correct to me. 
Although you can simplify it a lil’ more like this: 
Serial.print(x1);
Serial.write('\t');
Serial.println(y1);
I’m also noticing you’re sending 2 int values, not float 1s: 
int x1 = map(x, 1023, 0, -10, 10);
int y1 = map(y, 0, 1023, -10, 10);
So it’ll be more efficient to replace all float to int in the Processing side as well. 
Also in your Processing code side, I’ve spotted some bugs which wouldn’t be there if you had followed my own sketch model more closely! 
Where’s Serial::bufferUntil() after this statement: 
port = new Serial(this, "COM12", 115200);
And do not use Serial::available() when using serialEvent()! 