Bring 2 cups of water and 6 tablespoons oil to a boil in a large pot over high heat. Remove from heat and stir in flour and baking powder until well combined. Allow to cool, 15 to 20 minutes.
Add eggs, one by one, and then beat with an electric mixer until mixture is smooth and homogeneous.
Meanwhile, prepare the syrup. Combine sugar and 2 cups water in a saucepan and bring to a boil over medium-high. Stir until sugar has dissolved. Remove from heat and let cool, at least 20 to 30 minutes.
While syrup cools, heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).
Spoon dough into a tulumba syringe or an icing bag with a special nozzle and pipe small portions of dough into the hot oil. You can also drop spoonfuls of dough into the hot oil, but then the tulumbas won't have the traditional shape. Work in batches and fry tulumbas until golden, 5 to 7 minutes. Remove to a paper towel-lined plate. Let cool, about 10 minutes. Transfer tulumbas to a bowl and pour cooled syrup on top. Allow to soak for at least 2 hours.