The reason why I wouldn’t call it “invasive” in this case is because of the way it arrived and the fact that all species everywhere, other than the very first ones some 3.5 billion years ago, originated somewhere else.
The term “invasive” carries with it very specific baggage is is used inappropriately in many cases.
I work in environmental conservation and had a strong focus on environmental change in grad school. One of the big issues we face with climate change and global warming (which are technically two slightly different, but related things, the latter is what is happening and the former is the result of the latter) is that species need to move from where we are used to seeing them into new areas that are more suitable for living in as as result of shifts in the climate.
This is a natural process and takes place all the time all through the history of life everywhere, and not only in times of rapid environmental change.
We humans, however, tend to have a very narrow perspective in a temporal sense and think things should stay as they were when we started paying attention to our surroundings, and this spells disaster for the environmental near future (next few thousand years) of the planet as we are forcibly restricting natural movement of species and lumping very different things together and treating them the same.
An example: on Lake Camplain, the large body of water acting as the border between Vermont and upstate New York has traditionally been a place popular with ducks of various species. A while back cormorants moved into the area. These had not been previously been recorded in significant numbers right there (other than in their migratory season), but they’re the species that’s native to New England and widespread all through North America. The cormorants used some of the same nesting areas as the ducks in Lake Champlain, which caused people to start treating them like an “invasive” species and killing them (spraying oil on the eggs which kills the babies, but keeps the birds sitting on the eggs so that they don’t re-lay right away).
Thing is, they weren’t “invasive”. They were just doing what all species do, changing their ranges.
This range change is more and more common as we enter warmer and warmer climates, but we keep treating entirely natural movements of animals and plants as “invasive” even when they are simply a response to environmental changes. At the same time we are trying to keep certain species in areas that are no-longer suitable for them, and we have erected nearly insurmountable barriers to movement for many species, which will significantly impact their ability to adapt to a changing world.
Rafting events, as in the case of the aforementioned Japanese species, is also an entirely natural movement of species. Non-human primates are considered native to the Americas (South and Central America), but they rafter across the Atlantic in the past. Tortoises on Aldabra Island got there by rafting. Lemurs on Madagascar got there by rafting, on several different occasions from what genetic evidence tells us. All species that have colonized volcanic islands came from somewhere else.
None of those species should be considered “invasive”.
“Invasive” is reserved for human introduced (intentionally or accidentally) species that have moved beyond the “exotic” or “naturalized” state and pose harm to an ecosystem.