Both of you are still at it? Puñeta.
Yeah, it's pretty bad, eh? We have our pride.
Let's get back to topic, shall we?
How's Japan's logistics in case of an invasion attempt?
Great or terrible, depending.
They went most of the distance to take Taiwan, after all, coming from Weihaiwei and then later the home islands. If they're doing this per the OP, they've passed the two years of active resistance in Taiwan and had seven more to plant their feet there. Coming from Taipei the distance is very limited, the only question is what the state the local port facilities were in. If they're middling, logistics will still be workable; if they're good, logistics should be excellent.
That is modeled, though, on how Japanese navy could act when all its opposition was already resting on the sea floor. So if the Spanish keep their ships in the Atlantic or have lost them all, yes, Japan's golden. But if the Spanish are smart, they can give the Japanese a very hard time. If they bring their navy close enough to be a threat to a Japanese move anywhere in the region, but prevent the Japanese from catching it out and destroying it, the Japanese navy would be left with much less freedom of action. [Taking this from war-gaming what the Spanish should have done fighting the US in OTL, actually. The principle is the same.]
If the Spanish still have a fleet, the Japanese wouldn't be able to accomplish much beyond supporting the Filipinos if they rise up. That could be enough if the Japanese can afford to convoy their fleet back and forth, leaving arms and Japanese army units behind. But if the Filipinos are loyal for some reason, even in some large part, with logistics like that Japanese victory is actually pretty difficult to accomplish. They'd have to take some risks to provoke a fleet engagement, which could fail or even backfire.