Is the Shimano SL-M590 shifter compatible with XTR RD-M900 rear derailleur?
Your information is a little out of date, but for 9-speed, all road and mountain rear derailleurs and shifters are cross compatible from xtr and da to Alivio and Sora.
Other combinations work to but for the purposes of your question, there are no issues or likely problems from your component selection.