Google translate:
Sephiroth
"Mother's name Genoa.
Died immediately in the birth me.
My father ...... "
Immediately it says...
Google translate won't help you with Japanese. That can be translated many different ways and you need to understand the nuances of Japanese to get its meaning. There have been a ton of times where the literal comes out missing the point, but a Japanese person reads the line as it was intended to be read.
In all cases "right after" is a bad line for Sep.
すぐ 《直ぐ》 (adj-na,adv,n) (1) (uk) immediately; at once; directly; (2) soon; before long; shortly; (3)
This is why Japanese frustrates me... Immediately and soon are not the same thing, but seem to be used with this same "word". I am guessing the reason is entirely in how it interacts with the other stuff in the sentence (the context and nuances)... and that's where Google Translate is checking out.
However, if she did die "after giving birth" due to unrelated reasons, we'd say "Not long after I was born", not "After giving birth to me"