Short Answer: Not always!
The key is using the Drop app to launch the offer.
But if you tap on the Drop offer and are prompted to download/open the merchant app, you can make a qualifying purchase this way!
If you download the merchant's app, please return to the Drop app once it's done downloading. Tap back on the offer and get redirected this way. This will ensure that when you make your purchase, the points post to your Drop account automatically. ✅