I can see two possible causes, and it should be easy to work out which is in the frame. The problem is probably from the charging adaptor side rather than a fault on the Surface Pro itself.
1. Static discharge finding a path to ground through the device and charging cable to a grounded wall socket. This will be a one time instant hit like your "pin jabbed" then nothing more, and it is not a cause for concern except as a discomfort factor. You probably experience the same kind of static discharge sometimes when getting out of the car, or removing artificial fiber clothing.
2. Leakage of AC mains voltage onto the grounded screen of the charging cable, which is connected to the body of the device. You will usually experience this as a more prolonged sensation like your "mild tingle", and the intensity will depend how well connected your body is to a true ground/earth by some other route - like bare feet onto the floor. This is more worrying because it could be caused by a potentially dangerous fault on your wall socket, or by leakage in the filters of the AC supply charging adaptor.
Dealing with a faulty socket first, the things to look for are reversed hot and neutral lines, and/or the earth (ground) connection not properly connected to ground, or worse... having a cable fault on your house installation which puts live voltage on the earth line.
If the AC connection into the adaptor is a 2-pin plug without a ground connection it is almost certain to be leakage in the filters and power supply components. If the adaptor has a 3-pin connector and you are using it into an ungrounded mains socket (a 3 pin to 2 pin adaptor?) that could force designed filter leakage to go "the wrong way" into the body of your mobile device. You should be able to detect this easily by using a multimeter (a cheap one will do fine) on AC voltage range to check for volts when measuring with one lead to the outer shell of the USB connector and the other lead to a good ground connection. Anything above 1 or 2 volts suggests a problem.
If you have everything connected to a surge suppression multiplug block this will also have filters which are designed to dump surges onto the ground line, and there is always a tiny leakage in normal operation. If the input plug is not grounded at the wall socket this WILL cause problems by putting leakage voltage on the output socket's ground pin instead of allowing it to pass harmlessly to ground.