No they don’t have to be consumed at the same time.
In fact, I suggest taking 5g of glutamine pre and post exercise. Adding it to your protein shake is a good idea.
As far as BCAA’s, supplementing before can help reduce muscle soreness and help speed up the recovery process after a workout. I always suggest to use them during exercise to reduce fatigue and improve physical and mental performance, especially if you train in a fasted state. fasted = no food prior to training. There is not a lot of evidence that consuming BCAA’s after training actually leads to greater muscle mass in the long run. You are better off with a protein shake.
The best thing is to try different scenarios and see what works best for you. I usually consume two servings of BCAA’s daily. One when I immediately wake up and the second during training.
But bottom line, no, they don’t need to be taken at the same time.