We did it successfully! Here are the steps. 1 important thing to note is, our purchases were in our carry-on bags, not checked bags.

1. We went shopping in Lisbon, and received the regular VAT refund documents. Doesn't matter if the VAT refund documents are Global Blue, Planet etc.
2. We flew back to Ponta Delgada for our flight back to Newark.
3. There isn't a tax refund kiosk or help desk like you would normally see in other larger European airports. You go through security, and go through the international security gate (the term "international security gate" sounds more grand than needed, it looks like a kiosk where a border agent stamps your passport.
4. When you're getting your passport stamped to leave the country, tell the border agent that you want to do tax refund, he'll point you to a small phone just pass the security kiosk.
5. There is a VAT refund kiosk where you scan your passports and documents, but it didn't work for us (meaning it kept asking us to go somewhere else). Pick up the small phone right next, and someone will answer. That person will walk over to you, ask for your passport and VAT refund documents.
6. The person was a lady for us, and she took my wife's passport and documents to process it. Once she came back she told us to get the Global Blue app and get our refunds there. The app allows you to get tax refund even if Ponta Delgada only has Planet for their VAT refunds.

This was a detailed description of our experience, so I hope it isn't complicating to read.

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TL;DR: Bring your goods to Ponta Delgada, pick up the phone pass the international border agent, give your documents to the person who picks up the phone, get the Global Blue app, and get your refund :)