The problem with Twitter is that it's mainly mobile traffic.
Which sucks for conversion.
What people do is look at the Tweets with their cell phone, then when they get back home look for the item using their Laptop/Pc
There goes your commission...
Well it's not 100% bad tho
The only way i have found is to create a domain name about the product you are trying to push and THEN advertise this domain.
So people from Twitter will type in the domain name when they get back home