If I understand what you want to do correctly then a ShippingRewardApplicator seem a bit too invasive.

Creating a custom promotion with an attribute for store id and a custom processor should be the way to go:
https://world.episerver.com/documentation/developer-guides/commerce/marketing/custom-promotions/

You also should extend the shipment with a field for store id and set it when creating the shipment, that way the processor can check against that to make sure it is only applied to the correct shipment:
https://world.episerver.com/documentation/developer-guides/commerce/orders/Extending-order-classes/

This is of course assuming you want a shipping promotion, that is a promotion that gives a discount to the shipping cost.

If you want to give discounts to the actual items from a specific store then you should go for custom entry promotions and possibly extend the LineItem with store id if necessary.

Hi Erik, thanks for your answer.

Yes i am talking about a shipping promotions.

So far, i have created a custom promotion that has a StoreId property (is that what you meant by "Creating a custom promotion with an attribute for store id" ?), a custom shipping promotion processor, and yeah, our shipments already have a storeId informatin associated.

I am still in the middle of coding all of that, but the concern i am trying to address is what i read on the new Promotions page in the developer guide (sorry not allowed to add links) :

Note: If an order has several shipments, the shipping discount only applies to the shipment with the greatest shipping cost.
For example:
* Shipment 1 has a shipping cost of $39.76.
* Shipment 2 (in the same order form) has a shipping cost of $28.00.
If you apply a 10% discount, the discount amount is $3.98.

Decompiling some codes and lloking at what has been done, i think that i may select the shipment that the promotion is going to apply to by overriding the GetRedemtions() method :

protected override IEnumerable<RedemptionDescription> GetRedemptions(
    StoreFreeShippingCoupon promotionData,
    IOrderForm orderForm,
    PromotionProcessorContext context)
{
    var redemptionDescriptionList = new List<RedemptionDescription>();

    var shipments = GetApplicableShipments(promotionData, context.OrderForm).ToList(); // this is where the correct shipment will be selected

    if (shipments.Any())
        redemptionDescriptionList.Add(CreateRedemptionDescription(shipments, context));

    return redemptionDescriptionList;
}

Does this make sense at all ? Is this how "the processor can check against that to make sure it is only applied to the correct shipment" ?

That note is what will happen if more than one shipment is found and it is what happens for the built-in shipping promotions.

Yes exactly like that, with the GetApplicableShipments looking something like this:

IEnumerable<IShipment> shipments = ShippingPromotionProcessorBase<TShippingPromotion>.GetShipments(orderForm, (IEnumerable<Guid>) promotionData.ShippingMethods).Where(s=>s["StoreId"] == promotionData.StoreId).ToList();

Of course adapt it to correct data types if you have store ids that are integers or strings. (the context.OrderForm is a bit redundant as you already have the orderForm parameter. ;))
Most likely you have already worked it out by the time i post this. :D

Thanks for your precious help Erik. A bit busy at the moment, but will try that out asap and will update the topic if i have any more findings on this.

Cheers !