First realize that the main purpose of the truss rod is to make the strings parallel to the neck, the bridge is the primary control of action. If your open strings are buzzing then you need to loosen the rod, i.e the neck is backed bowed. This makes sense if you down tuned your guitar, since you have less tension on the neck, it is now backed bowed. Only make small adjustments on the nut, like 1/4 turn at a time, some guitars can only have their truss loosened so much. Tune it first then adjust the rod, then set the action via the bridge. If you loosen it too much you will have buzzing when playing in the middle of the fret board. Your goal is to have a slight bow in the neck but not much.
Here is the process. Fret your 6th string on the 1st fret then with your other hand fret around the 16th fret (where your neck meets the body), then with your index finger of your right hand tap on around the middle of the fret board (6-9 fret). You should have a little space there you can also just look at it and just see a slight amount of space (0.3-0.5mm).
If you are not comfortable doing this then don't, you can mess up the neck if you over
adjust (so I've heard). However if you learn what your are doing and why you can save your self time and bucks. I make small adjustments to my truss rod throughout the year as the
seasons/humidity change.