The western North Pacific averages about 25 typhoons a year, on the Japan Meteorological Agency's 1991–2020 figures. Unlike the Atlantic, there is no official start or end date. A few storms form even in winter, but most form from July through October, and August is the busiest month.
For Japan, the storms bunch up in late summer. On average about 12 typhoons a year come close to the country and 3 make landfall. August and September each bring more than a quarter of the close approaches and, between them, most of the landfalls. Taiwan, the Philippines, Okinawa, Hong Kong, and central Vietnam lie closer to where the storms form, so a sailing there in June or November is also worth watching.
Cruise lines handle typhoons the way they handle hurricanes: they change the route days ahead, skip or swap a port, or stay an extra day somewhere sheltered. A typhoon can also close ports and airports for a day or two, so build some slack into flights home on a sailing between July and October.