Japanican is a company in JTB group - the largest agency in Japan. They are as reliable as a travel agency can be. If you were able to book through them when other sites showed no availability, it may be because JTB has its own deals with hotels etc.
https://en.wikipedia.org/wiki/JTB_Corporation

There is always a chance that a hotel will overbook and walk some guests, but it's pretty unusual in Japan. And in the event that it does happen to you, I expect Japanican to be responsive and supportive.