And what you're experiencing with Streets of Rage 2 is also normal. The game uses a special high resolution mode in PAL, which causes the screen to roll when used in NTSC. Fortunately, SoR2 switches the resolution when going from the title screen to the menu, so that fixes the rolling. Alternatively, you can start up the game in Japanese mode, and switch to American while the game is running.
You can see this too in the demonstration movie I made of my first prototype single-switch mod: