Hyperdia Routes?

I was searching up a route from Nishioji to Keage station in Kyoto, and part of it routes through Kyoto station with the grey arrows (which I understand means that I should just stay on the train). But going into the station it lists one train line, coming out it's another train line. Does that mean that the two lines connect to each other? Will I need to stay on a specific train car to avoid going in the wrong direction?

Just to make sure: Is Nishioji Station really near your stating point?
Nishioji is a north-south road in Kyoto City.
There are several stations along this avenue.

It seems you are asking about a route via (JR) Yamashina Station.
http://www.hyperdia.com/en/cgi/en/search.html?dep_node=NISHIOJI&arv_no...

JR Rapid trains departing from Nishioji Station at Track 3 go
by JR Kyoto Line until Kyoto Station
then by JR Biwako Line via Yamashina Station for Maibara.
Catching a Rapid train, you don�ft need to change trains at Kyoto Station.

Note
: All Special Rapid trains and some Rapid trains skip Nishioji Station; please be careful when you plan to take a train to this station.

Yamashina Stations of JR and Kyoto City Subway are close to each other;
from the JR concourse you can go down
(by elevator | escalator | staircase)
to the slope leading to the subway concourse.
Subway trains for Keage depart from Yamashina Station at Track 1.
https://www.jr-odekake.net/eki/img/premises/0610115.pdf
http://www2.city.kyoto.lg.jp/kotsu/tikadia/img/map/sta/pdf/t07map.pdf

Nishioji: Here "o" is pronounced long.
Keage: This name has three syllables (Ke-a-ge).

Yep, Nishioji Station is the nearest station to my accomodation and there's no other station nearby. Thanks for the clarification, especially about special rapid and rapid trains, I think I'll have to be extra careful when going back then!

Is this not enough?
https://goo.gl/maps/o6GcerCqiWJ2
Change date and time.

And, you can paste here the link as full long URL of the result, like this.
http://www.hyperdia.com/en/cgi/en/search.html?dep_node=NISHIOJI&arv_no...
So, which date and time input?

And more, other way of route search web exist but this is only for Kyoto City,
http://www.arukumachikyoto.jp/index.php?lang=en
also their free app is very covenient if you have a cellphone or tabletPC(iPad or).