Some tissues are and some aren't. There are certainly papermakers who still make tissues by hand – and in fact, creating a uniform whisper-thin 5g tissue (think a single ply of facial tissue) – is still considered the sign of a master papermaker. But the labor in material preparation and years of practice to train the hand and eye is formidable, so they are comparatively expensive and tend not to be very "flashy." Not surprisingly, perhaps, they are therefore less popular than their machine-made counterparts.
The tissues LCI carry are all machine-made variations on traditional Japanese tissues in a variety of contemporary colours. Because they are machine-made, they are much more economical and therefore far more popular. You might be interested to know that all of LCI's tissues are made by one company, a small family-run "factory" studio in Japan. (We use quotation marks because, while it is mechanized, their small facility is a far cry from the massive facilities we associate with the term factory here in North America! It's like the difference between a small neighbourhood green grocer and a massive supermarket.)
