There is a great deal of confusion in the use of occidental and oriental in the literature, including the old writers.
There is no single definition for the terms, and the meanings are often contradictory. Great care to understand what an author means by "oriental" must always be exercised.
You have understood "the planet of oriental rising" as "the oriental planet". Your sources have not explained things fully.
"Oriental rising" is based on the diurnal motion of the Earth (primum mobile). For example, if Mercury rises before the Sun does (near dawn), then it is "oriental" to the Sun. The oriental planet "goes before" the Sun, acts "in advance" of him and so on. We might say that the planet of oriental rising is the herald of the Sun, goes ahead of him announcing his coming. The Sun's rays, or presence, emerge into the world through this planet of oriental rising.
I think some of the modern authors have overblown the importance of this position.
I'm not goiing to go into all the ins-and-outs of oriental and occidental here. You need to study this on your own.