Cook rice according to package directions. Spread on parchment paper-lined tray. Let cool completely; refrigerate for 1 to 2 hours or until thoroughly chilled.
Meanwhile, toss together tuna, 3/4 cup lime juice and half of the salt in a glass bowl. Cover and refrigerate, stirring gently with a plastic spatula every 15 to 20 minutes, for 45 to 60 minutes or until tuna changes color slightly. Strain tuna mixture, discarding liquid.
In a separate bowl, mix together mangos, cucumber, red onion, cilantro, orange juice, jalapeño, and remaining lime juice and salt.
Just before serving, gently toss together marinated tuna mixture, jasmine rice, mango mixture and avocados. Transfer ceviche to a serving bowl or individual serving glasses.
To make tuna easier to cut, freeze for 30 to 40 minutes before cutting into cubes.
Substitute tomatoes for mangos if desired.