Confusion regarding the design of Lithium Ion PCB
The PCBA that you give as an example is intended as a protection unit that will (attempt to) save the battery from excesses of treatment by the system.
It assumes that a "proper" controller will handle the actual system management and that its role is as an emergency watchdog.

If its parameters were set conservatively it might interfere with design decisions made by a system designer for the main controller. As this unit is usually hard connected inside a battery pack, having it stop the designer doing sensible things would be "a bad thing" [tm] SO it is set to values that no sane designer will reasonably approach. 

If you rely on it as the main controller your battery's days will be short on the face of the land.
eg 4.35V +/- 0.025 V for Vmax during charging will at minimum greatly decrease available battery cycle lifetime and worst case will set remaining cycle lifetime to zero.

V_min_protection at 2.4V is unlikely to be fatal but will decrease cycle life if used regularly.

The "restart after protection operates" values gives a good idea of what the designer of this protection board think that you should REALLY be doing - ie 4.2V recharge restart and 3V discharge restart.  These correspond to typical industry practice for actual limiting values.

ICs intended for actual battery management in systems will use end point values around 3V and 4.2V.