If I purchased their product, I've initiated a relationship with this company and I do not mind the follow up e-mail.
It isn't a "followup" since there is no human behind it, and there is generally no way to directly respond to the email. It is just machine generated spam, trying to generate a statistical response. If I receive one message, I delete it. If I receive another from the same vendor, I go to Amazon and give them a one-star review. If you do this too (and I hope you do) then do NOT mention the spam as a reason for the bad review. If you do that, Amazon will remove the review, since reviews must be about the product and not the company selling it. So just make something up instead.
If enough people do this, the spam will stop.
An even better solution would be for Amazon to allow the customers to opt out of having their email shared with vendors.