In general, all pure Japanese Tokugawa clocks use the verge escapement, with initially the single foliot balance, followed by the double foliot balance, then returning back to the single foliot balance with namagata or waricoma dial. This is equally true for lantern style clocks and shaku-dokei.
Whilst the same verge escapement was retained, the balance was developed first with the pendulum, followed by the balance wheel and finally the balance wheel with hairspring. These escapements appeared about 70 years later than their European counterparts.
It does not appear that the clockmakers got a chance to copy the balance spring directly or, perhaps, they did not fully understand its purpose. They produced what amounts to a free-sprung balance which was brought to time by two weights sliding along the balance arms after the manner of foliot weights. The spring itself had very little resilience being formed out of iron wire into three or more turns by hand. Curb pins arrived somewhat later and are usually found in watches or clocks in conjunction with a vertical balance and European type bridge.