I guess it is a joystick issue which is not quite accurate and which causes false contact if the lever is slightly pushed down. I bet that with a Competition Pro (my absolute favorite joystick) the problem does not arise. I can also assure you that moving left or right does not reset the down position of the lever in any way; to teleport a second time you have to release the lever from the down position and then push it down again.
Regarding the other problem, I tried to emulate an NTSC C128 on PC but I didn't find anything strange.
In any case, I'm glad you enjoy the game; I just recommend a more suitable microswitch joystick.