Let's see if I got this right...
Renton and Eureka--still pregnant with Ao--was messing with some Scrub Coral when it suddenly sends Eureka and Nirvash back to the Ao world of 2025. This is the Eureka we see in this episode (13).
At some point after episode 13, Eureka is sent back to 2012, where she gives birth to Ao.
By 2015, Eureka assists the chief and his fellow troops in fighting the Secrets. She remembers the chief and that other guy because she already met them in the future in this episode.
What happened to Eureka after that battle with the Secrets in 2015 is still unknown.
Am I getting this right?
Yup. Pretty much.