It is possible that the golf scene was played in the proper order. Sayid was able to kill the Italian without any witnesses and without leaving any clues that it was him. The man looked terrified when he found himself with one of the Oceanic 6, because of his own involvement in the Oceanic cover up. He may have known someone was killing those involved. Casually running into one of the six would be more than a coincidence.... so he showed proper fear.

I think Sayid said "now they know I am after them" after he shot Ilsa because she had knowledge of who he was and what his mission was and she had been reporting it to the economist. Now the identity of the assassin is common knowledge amongst those he is hunting. Before they may have suspected it was one of the six, but were not for sure which one.