Generally, Dolphin "Encounter" means that you will not be in the water swimming with them, that is how it is in Nassau and Freeport (you are on a ledge about waist deep and the dolphins come to you)... However, the Shore excursion description provided BY Disney for the excursion you are looking at says that it is in fact a "SWIM":
Anguilla Dolphin & Stingray Encounter (7 - 7.5 hours)
You will get the opportunity to feed and touch stingless stingrays before you swim, feed and play with dolphins while learning fascinating facts about them. There will be plenty of photo opportunities, so don't forget your camera (underwater cameras are not allowed in the water). For a perfect ending to a memorable morning, take time for fun and sun on the beach at beautiful Meads Bay, where you can enjoy an authentic Caribbean barbecue lunch.
Adult Price: $180 (ages 10 and above)
Child Price: $158 (ages 5-9)
Departure Time: 7:30 am