In the manga, how did Asako contact Ushio from within the sea serpent?
In both the manga and anime, Tatsuya had a precious gift from his mother.  In the anime, it was referred to as a toy phone.  In the manga, it was a functioning walkie talkie (referred to as transceiver in the English translation).  There just happened to be someone on the beach with another transceiver who was listening on the right channel.  Asako's call for help was heard by Ushio.

What I found difficult to understand is why Asako's plea was even needed as part of the plot.  The sea-protector yokai had already informed Ushio that Tora needed his help and had been swallowed by a giant serpent.  That could have been sufficient cause for Ushio to help.