I am wondering if the study got the timing of the day lengthening events properly associated the climate events.
The tidal forces of the Earth's oceans on the Moon's orbit, which tend to accelerate the Moon's velocity while decreasing the Earth's rotation rate, should be influenced by how much water is in the oceans. So, it makes sense that during warm periods of Earth's climate, with most of the water in equatorial oceans, the effects would be strongest, while during periods of global ice sheets with reduced liquid water in the oceans near the equator, the effects would be weakest.
But, this article puts one day-lengthening step in a hot climate period and the other in a cold climate period.
So, that makes me wonder if the ages of the steps and the climates were derived from different types f data and may not be adequately correlated.