Whether or not you decide to allow affiliates to purchase through their own link is completely up to you. If you want to promote your product this way you should mention it on your affiliate info page since many sellers do not want affiliates to purchase through their own link.
If you do not want to pay commissions to an affiliate who purchased through their own link you will need to ban the affiliate from promoting your products. Banning should only be used if you feel that the affiliate has broken the terms of your agreement. Posting your terms on the affiliate info page is one way to manage expectations.