Was I being stupid of connecting this charger to this device which states that it should be connected to 5V charger?
Technically, no, you were not bring stupid.
The charging capacity of the charger can be larger than the device so long as the device conforms to the charging specifications.
Within few seconds of connecting, steam started coming out of the charging case.
That’s not steam. It’s the “magic smoke” and you let it out. In all seriousness, the case got burnt to a crisp.
Now, if the charger is USB-C, one would assume that it’s compatible with other USB-C type chargers that conform to the USB PD (Power Delivery) specification. It sounds like this device doesn’t. Reading the user manual, it doesn’t list USB-C PD, but refer to it as a “Type C charging port” (page 3). This is very misleading because it makes you believe you can use a USB-C charger with this. In fact, you can only use a standard USB charger that only outputs 5 volts.
IMO, this is a horrible design. They should have used either a USB mini port or USB-C that conformed to the Power Delivery specification. Now, the USB Power Delivery specification has four normative voltages: 5V, 9V, 15V, and 20V. The charging device will negotiate with the charger as to how much voltage to deliver. By default, it supplies 5V. So, it should work. Since it got fried, this is clearly a case of a faulty design or manufacturing defect of the charging case.