Pineapple Ground Cherry Seeds. Start seeds in a very warm location 8+ weeks before planting. A heat mat will speed up germination (an oven-proofing drawer is even better). Seeds can be slow to germinate and can take 4+ weeks. Germination is sporadic; some may germinate at 3 weeks and others at 6 weeks. Harden off (take the plants for increasing amounts of time and light) for a week before you want to plant out. Harvest continues until frost. Ground Cherries are in the tomato/tomatillo family. Plants grow into stocky plants that do not need to be trellised. Pineapple ground cherries taste like cherry tomatoes with pineapple juice infused in the berry.