Like i said, beside BMS, i will add temperature and current fuse. But yes, i understand the problem. I am wondering, overcharge (voltage over 4.2V). Why does the battery explode ? Does it heat up or not during that charge to high voltage, for instance 4.5V.
Lithium is a highly reactive metal, and burns easily.
The protection board, along with the correct 21V charger, will do everything you need - temperature monitoring is only really required if you're attempting to charge the batteries very fast, in which case you need to monitor their temperature, and drop the current if they get too hot. I originally build LM35's in my battery packs, but as I wasn't fast charging them I never used them, so have stopped fitting them now.
The protection board provides over current protection, making a fuse not required, although it's never a bad idea to add one. I use one on the DC input for the charger circuit (as it charges from a 12V car battery).
Charging Li-Ion is pretty easy, you need a constant voltage source (21V in your case) that does current limiting - these are easily and cheaply available as modules from China. Set the voltage to 21V, the current to what you want, and connect to the battery - this is all included in the ready made mains charger you looked at.The charger will supply the constant current to the battery, and the voltage will rise as it charges, once it gets to 21V the charger will switch to constant voltage, and the battery is fully charged. The protection pack on the battery takes care of any other issues, and will probably disconnect the charge slightly before it's 100% charged, for safety reasons.