Plug in the charger the wrong way? Yesterday, I mistakenly tried to push the charger plug in my phone upside-down. 

The phone seemed to react to it. Does it matter which way the plug is turned for charging?
Yes, it matters. The pins on a micro-USB connector are inside, and they're only on one side of the connector, so you can't get power or data through the connection if it's upside-down. If you got a reaction, it was probably just from the outside of the plug, which is connected to ground. If you're pushing it in hard enough to do that, you're probably damaging the socket, so try to avoid doing that in future.