The cheap US adapter is highly likey to be the problem, causing slower than expected charging.

USB charging (and USB ports on computers) has precisely one output voltage, 5 volts. This is fixed, regardless of the AC mains voltage.

USB chargers vary from the bottom tier rating of 2.5 watts (while 5 watts is common enough, it is not the lowest/cheapest level) up to 10 and 12 watts.

The limit on charging speed (Amps current) is determined by the LOWER of the maximum output the charger can provide or the maximum rate the device can absorb power.

There are other reasons to avoid cheaply made USB chargers. One is safety risks. It is not unusual for inexpensive chargers to have poorly designed or poorly manufactured electronics which create risk of electrical shock or fire.

Another potential problem is electrical interference. If the USB charger is creating 'noisy' DC power then it can affect the operation of the touch screen device. I once had a car charger that made my iPhone react crazily to finger touches. That charger got binned shortly afterwards.

When I travel I carry a name brand dual output USB charger that is rated for the full 2 Amps (10 watts) charging on each port.

Top grade USB chargers can be hard to identify as the lesser powered dual port chargers also label themselves as '10 watts', but that is for both ports combined.

BTW, I am in the market for a compact/portable/travel sized four port USB charger that provides Apple compatible 10/12 watts on each of the four ports. If someone has a recommendation, I am interested.