Do tiered discounts apply to regular orders not placed through rePete?

No. Tiered discounts created in rePete only apply to reorders placed through a rePete order channel. While all reorders are counted toward the customer's tier progression, the discount is only applied when they reorder through a rePete channel.
 

Note: When ordering via the product page rePete Buy Button, customers will receive the rePete discount that is applicable on the first order count only. Read more about this in rePete Buy Button.