Quick Charge phone dont explode. I own quite a few of them, they just heat up quickly, but never explode, normally wont use the phone while charging.
No support quick charge means is no support. It is a good to have feature, less charging time is better. Confirmation of quick charge support usually from the phone manual or direct measuring the charging voltage and ampere using are USB voltage/ampere measuring tools, this is the most accurate measurement. Some 5000mah with Qualcomm QC actually charged around 2 hours. So, meaning this phone will charge over 3 hours.
There are only 4 most common quick charge. Qualcomm QC is the most adopted standard, most brand supported, but not all ( Motorola/Samsung/LG/Xiaomi/HTC/Lenovo/ASUS) , the certified charger is compatible to all supported phone, regardless of brand and charging cable. There are phone that supported the Qualcomm QC, but not including the charger right out of the box.
Again, just need confirmation for QC. I rest assure it wont explode, and actually comes very handy when we want quicker charging.