Whisk together juice, chile purée, onion, and 1 1/2 teaspoons salt in a large bowl for marinade.
Halve squid tentacles lengthwise and cut bodies (including flaps, if attached) crosswise into 1/4-inch rings.
Poach scallops and shrimp in a medium pot of barely simmering water, stirring occasionally, until barely cooked through, about 1 minute. Stir in squid and cook, stirring occasionally, until just tender, about 40 seconds.
Drain seafood well in a colander and add to marinade. Marinate, uncovered and chilled, at least 3 hours (for flavors to develop).
Just before serving, stir in cilantro. Spoon seafood into shallow bowls with a slotted spoon, then spoon marinade over it.
Cooks' note: Ceviche can be chilled up to 8 hours (cover once cooled).