The Otomo were still huge traders with Europe, mainly Portugal, correct?
At this time, Portuguese carracks come once a year bringing silk, porcelain, and other goods to Japan, in exchange mostly for silver. They bring guns, too, but by 1545, Japanese had learned to make arquebus (but they are still not in general, wide production, and are thus traded throughout the clans).
The reason these carracks come is that the Chinese have outlawed trade with Japan on the basis that the wakou pirates were causing the Chinese a lot of distress during this time period. Since Macau was acquired about 5 years prior to our start date, the Portuguese are effective intermediaries to bring valuable, highly coveted Chinese goods to Japan. Trade with China is thus a bigger drive for economies at this time - trade with China, through Portuguese intermediaries - and not trade with Europe. Trade with China is huge in understanding wealthy clans and their ability to feed, say, an entire army.
That said, the Europeans are not trading exclusively with any single clan, and even if you read some history saying that they are trading with Otomo or Arima or Shimazu, while this is true, the European carracks were also distributing goods to merchants and these goods were quickly dispersed throughout all of Japan, going in bulk to the highest bidders (which were the wealthy clans that you all play as
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). There are exceptions, of course.
If I remember correctly, the Portuguese even had a system in which most goods from a single carrack go to the highest bidder once a year. But I think this was more symbolic, and that the goods were often pushed through many different merchants and clans - perhaps originally being bought by a wealthy family, they were never hoarded as that would lack the most profit available. That is now the Oda received silks (and other clans in Kanto). But it is important to remember that Portuguese ships did not only go to Kyushu, and that goods from China permeated all regions of Japan.
edit: I should also mention that I am generalizing trade in this game for the sake of simplicity (and because the turns move through a whole year). We won't be dealing with where the Portuguese carrack is docked and where the goods went first or anything like that.