Private Rates that a that lower the SP Effective Cost of an Instance lower than the List SP Effective Cost from - https://aws.amazon.com/savingsplans/compute-pricing/ won't be reflected in the Savings Plan Recommendation tool.
The Savings Plan Recommendation Tool makes use of the List Price from AWS when generating a recommendation this also means that EDP and Discounts introduced via a Custom Pricebook won't be reflected in the Savings Plan Recommendation Tool.
To verify if you are receiving a Private Rate for SP Effective cost, create a FlexReport and narrow the returned data down to a specific instance of a certain type and comparing the Savings Plan _ Savings Plan Rate field to the Savings Plan Rate returned under - https://aws.amazon.com/savingsplans/compute-pricing/ for that same Instance Type.