Using amazon attribution on a website?

I work with a brand that drives their traffic to amazon and other sites where their inventory is sold, for a long time it has been a mystery as to what % of the traffic is actually converting from the website on amazon.

With amazon attribution, there doesn’t seem to be a “publisher” that can be listed as the brands website, but there is the option for “new”. If we link the button on the brands website using the attribution tag URL, will we be able to track the conversions on amazon from traffic that visited the brand website first?
Does this go against any of their policies? In theory it seems like it should work since the attribution tag functions similarly to UTM parameters in a URL, but worried that amazon has some policy i’ve overlooked that prohibits this.