Summary: Royalties are earned on every t-shirt sold and calculated based on the day the product ships out, not the date of sale. Shirts generally ship out 3-5 business days after the sale is made. Note that this can extend to 5-7 business days during high sales periods.
These royalties are based on the list price you set when creating the product, minus both a listing fee by Amazon and the cost of Amazon completing the product order (materials, printing, fulfillment).
Current information on royalties can be found in our Merch by Amazon Overview:
Royalty Calculation: https://merch.amazon.com/resource/201858580