I ran into this while trying to use the complimentary one-way airport transfer promo (see screenshot below) and while K and I were checking out at TGM, got to listen to another guest complain to the front desk about the issue I had. Yes, the free one-way transfer from PUJ to TGM does exist - we were able to get it, but it takes work. After you make your reservation and pay for the stay, email Reservations (Premier or regular) to request booking the one-way transfer and include your flight info. If they direct you to a booking link and tell you that "payment info is requested but you will not be charged" - that is not the case, the Paypal buttons do in fact charge your credit card. If this happens, INSIST that they make the reservation on your behalf - this is what happened to me, after I emailed them back that I was charged. Feel free to email back that "this happened to a friend who was charged and had to dispute the credit card charge" If you do end up getting charged, dispute the charge through your credit card company. I put this on a Chase Sapphire card, and Chase did eventually reverse the charge. You should receive an email confirmation directly from the transfer company with the trip details and Zero dollar receipt with the $150 charge and a $150 credit.
All that said, there was another post on the forums here that suggested using Expedia to book the airport transfers. @Ragekage used that for our return trip (TGM to PUJ), and the price was $80 each way before tip vs. the $150 when booking through the hotel's preferred vendor. The premium service uses a Chevy Suburban vs. our return car was a Kia SUV. No big deal/difference, imo.