Yes, that is correct. I wrote what happened to Ruma when Vali was killed. I did not write about Tara. After Vali's death, both Ruma and Tara lived with Sugreev. In fact, Vali himself, just before his death, suggested to Sugreev that Tara should live with him and he also said that Tara gives very good suggestions.
Laxman very angrily went to meet Sugreev. Tara came to calm down Laxman. She spoke sweetly. Moreover, she was a woman. This camled Laxman.