In How to Use: XIII, in the second point it says
The god of Death always remains with the owner of the Death Note.
indicating that a Shinigami will remain with the owner of their Death Note, Light learns this and gathers a group of friends to try and hide himself with Ryuk following him when Misa is trying to find him (she finds him because of her Eyes)
However, the Death Note Light had in the beginning isn't Ryuk's but Sidoh's which Ryuk stole, and unlike Gelus who died and Rem probably obtained ownership of Gelus's Death Note afterwards, Sidoh was still alive so even if Light became the owner after Ryuk dropped it in the human world, the Shinigami who was supposed to be with like was Sidoh.
Also in How to Use 2, the second point says
The owner of the note can recognize the image and voice of the original owner, i.e. a god of death.
So is there an explanation as to how Ryuk was tied with Light's Death Note having stolen it from Sidoh?