In the Instant Pot, combine the water and black-eyed peas.
Secure the lid on the pot. Close the pressure-release valve. Select MANUAL or PRESSURE COOK and set pot at HIGH pressure for 10 minutes. At the end of the cooking time, allow the pot to sit undisturbed until the pressure has released. Drain any excess water. Allow the peas to cool slightly.
Meanwhile, in a large bowl, whisk together the olive oil, vinegar, cumin, lemon juice, salt, and ancho chile powder (if using). Add the black-eyed peas, onions, tomatoes, cilantro, and jalapeño to the bowl. Stir gently to combine.
Taste and adjust the lemon juice, vinegar, and salt as needed. (Resist the urge to oversalt at this point, as the salad will get saltier as it sits.) Allow the salad to rest for 1 hour or so at room temperature before serving.