The reason for the delay is, and without being too technical, to change the product pricing, the app sends a series of requests (API calls) to Shopify to get the product, set the compare at price, change the product price, and a few other tasks. Shopify has an API call limit, throttling how many updates can be done within a period of time.
General rule of thumb we use is it takes roughly 1 hour per 1000 variants to apply the discounts.
If you had 1000 products with 1 variant, or 100 products with 100 variants each, that would take around an hour for the sale to start, and also take another hour for the sale to end completely.
Can you make it go faster?
Their platform puts restrictions on the number of requests that a store can make in a given period. They also have request queueing on their side, so even if we push the data faster, it could take an extended period of time for their servers to process the request.