Work Visa with a Young Company

So I'm in the process of looking for new work. I've worked as a graphic designer in Tokyo on a humanities visa for a little over two years, but I'm looking for a change. I've interviewed at a number of places, and even gotten a few offers, but haven't really felt the right fit so far.

I applied to a magazine layout design company yesterday, and got a call back for an interview tomorrow. I liked their work and website which is why I applied- however, in reviewing their company profile, I realized that the company itself is only 3.5 years old. (The management level staff have a ton of years on experience in the industry, though)

The work I would be doing would still fall under the humanities visa, but could I possibly face trouble in getting permission to work here because of its relative "newness?" I'm assuming that comes into play as the stability of the position could be questioned. Are they fairly strict when transferring jobs?

company age doesnt matter as long as they are legal and would provide required docs