I'm going to answer you here, Jovan.
First, you're not the only one looking to find out about Asama drums. I have found some others,
and these people have more questions than answers. There's not much information out there. I have reached some conclusions, but I can't prove much.
Second, I believe that Asama Percussion was a Japanese business. One of the largest volcanos in Japan is named Asama, and lots of things are named after it, like ships and bullet trains. Why not a percussion company? Can't prove it tho.
Third, Asama sold drums, drum synthesizers, and music synthesizers. But I don't know if Asama was a manufacturer, distributor, or and off-brand for another manufacturer. There were also Asama guitars, but I don't know if Asama Percussion made those. One guy owned two Asama guitars, and he was asking his forum if Asama was a manufacturer or a brand. No one replied.
The Japanese Drum Museum offered some information which may explain this, or may not:
Paraphrasing, it says that in 1961 Pearl built a huge factory to meet the worldwide demand for drums due to rock 'n roll. The drumsets were cheap and bore the name of the distributor, namely: "Maxwin, CB-700, Crest, Revelle, Revere, Lyra, Majestic, Whitehall, Apollo, Toreador, Roxy, Coronet, and others -- over 30 brands in all! Tama, also known as Star and Hoshino back then, also followed suit . . . . many of the models were sold under many different names or badges." So, could Asama have been one of these distributors or brands? Maybe so. Not sure.
In 1962 the Hoshino Gakki company in Nagoya, Japan established TAMA Seisakusho Inc. and started to manufacture drums, guitars, and amps. These drums were not called TAMA. I don't know what they were called from 1962-1964. Starting in 1965 they were called STAR drums. And starting in 1974 they were called TAMA. What were the 1962-1964 drums called? Wish I knew.
But from 1974-1977 TAMA drums made "stencil kits." In other words, they made the same generic drums but put lots of different names on them. Could one of these names be Asama? And since TAMA Seisakusho also made guitars at this time, might they have named them Asama?
Given the similarity of TAMA and Asama drum fittings noticed by yourself and be the woman mentioned below, it is possible or even likely that Asama drums are one of the TAMA stencil kits. The TAMA stencil kits were not sold in Japan but were shipped to the USA and Europe mostly. None of the TAMA Seisakusho Inc. drums were sold in Japan before 1980. Maybe that's why you're finding this kit in Macedonia with the name Premier on it. I also saw a kit for sale online that was called Hohner Asama.
I found a picture of an Asama drumset online. The page is written in a foreign language -- don't know which one. But the title on the page is:"Batterie Asama idem TAMA." I'm pretty sure "batterie" means drumset. Can someone decipher the rest? Also, check the badge. I believe this set is for sale in Europe, so now we're looking at a TAMA Asama kit available in Europe. I think. This page is at: Batterie Asama idem TAMA Instruments de musique Oise - leboncoin.fr
Maybe the best thing I have for you is this next page. A woman has purchased what she believes to be an Asama kit. She was attracted to it because the fittings look like TAMA fittings, and she loves TAMA.
This page has GREAT PHOTOS, GREAT CLOSEUPS! Vintage Drum Museum • View topic - ASAMA drumkit - help needed with identification
Now, go to this page, scroll down, and check the badge and drums on this Asama kit. Drums My Life - drum forum, drummers community - View topic - Asama Percussion?
And if you were in the TAMA Seisakusho Inc. factory stenciling different names on drumsets, why not name one Asama? The volcano is a famous Japanese landmark about 150 miles from the factory.
As far as Premier goes, it may be that Asama drums were distributed to whoever wanted to sell them in Europe and America. Maybe Premier sold them as a second line. It sounds possible, but I have no idea whether it's true.
So the seller may not be lying to you; Premier may have sold those drums. But, of course, I really don't know.