The SwinSID doesn't drive the bus during reads, so the value read from the POT lines is kind of random. That can indeed be interpreted as second button presses by a game, if the scond button support is always active.
Yes, you're right. Based on a previous message from "radius75" : "The game uses potX/Y for additional Fire on Joystick port 2. (Fire 2 = Jump/UP)" so, maybe this generate the signals on POT lines, that cause the character jump continuosly when SwinSID is present, even if the joystick ports are free, nothing connected to .
As you well know, today it's quite difficult to find the original MOS SIDs as spares, and many are using the SwinSID, but right now it's not compatible with "A Pig Quest".