It is probably because the little Ema's mind in this parallel world is too fragile that the time-traveling girl took advantage of it and became a "shield" sub-personality. A shield probably means dealing with all messes, and abandoning all personal preferences to cater to the main personality. More importantly, help the main personality who will not refuse to deal with the male creatures in the family. She can probably be the most tired of the time-traveling girls.
Learning a skill you're not good at at all? No problem, just enrich yourself; deal with your "love rival"? It's not a big deal, at worst, she will act as the little white flower behind the brothers; "share" the love partner with the protagonist? Um... Just, give it a go.
Although she has little fighting spirit and is basically pushed forward by the plot, Rio believes that one day in the future, she can exist as her own unique identity.