In my opinion it is best to use tea tree oil as a spot treatment rather than all over your face. You don't have a lot of blemishes so it should work well that way. If you want to put moisturizer on top of the tea tree oil a gentle moisturizer might be best rather than one with salicylic acid so you don't irritate your skin.
You could always wash your face in the morning and then apply the moisturizer with salicylic acid. Then in the evening clean your face and apply the tea tree on certain spots and maybe just leave it (ie. no moisturizer at overnight). I don't know your skin so if it is very dry then maybe you need moisturizer overnight, sometimes you just need to try things for a bit to see what works for you.
Just my two cents worth!