From what we understand, using Jump Send's email campaign feature to ask customers for a review (who have already purchased your product at a full price or a discounted one) isn't against Amazon's Community Guidelines. Those consumers are not being paid or coerced in any way. If they choose to leave a review for your product, it is because they decided they wanted to do so.
We take Amazon's TOS very seriously and, due to the policy change with respect to reviews we do not require or request reviews in exchange for discounted products.
In addition, we do not permit reviews or votes on the helpfulness of the reviews left in exchange for compensation of any kind. That includes payment (whether in the form of money or gift certificates), bonus content, entry to a contest or sweepstakes, discounts on future purchases, extra product (buy one, get one), or other gifts.
We will continue to stay current and within Amazon's TOS and we will update our own policies so that they stay in line with Amazon's Terms of Service at all times.
Here are Amazon's TOS from their website as well, in case you wanted to have a look: Amazon's Terms of Service