To clear some things up - there is no such thing as a "tourist visa".
A visa is something you arrange before coming to Japan. When you arrive in Japan, immigration will look in your passport - if you have a visa then 99% of the time they will allow you into the country, and give you a status of residence that matches what the visa was. So if you have an "Instructors visa" you would receive a one or three year status of residence - instructor.
This means you can stay in Japan until the status of residence expires, doing whatever is allowed by that status of residence (in this case, teach).
Visas cease to exist the minute you go through immigration.
A "tourist visa" is when you have no visa in your passport, and you are given a short-stay status, where you are allowed to stay in Japan for a short period of time, with restrictions such as you are not allowed to work etc.
If you want to work, then get a proper visa. Theres no excuses, if you don't qualify, then make yourself qualify for one.
As someone else said -
if you leave Japan while a change of status of residence is being done, your change becomes void, and you have to start from scratch.
If you have a pending stamp in your passport, that is just as good as having a complete 'status of residence' stamp as far as immigration is concerned. I had a funny situation last year when I filed for a renewal the day before my expire date, and for over a month had to carry a passport and alien card that in essence said that I was "illegally overstaying", except for the vague and open ended "pending" stamp
Its the person who is going to employ him, and is doing his visa change. Doesn't mean they are paying him yet.