This is Gasoline Direct Injection system right?
If so, what you are seeing there looks normal to me.
I am not familiar with this application but typically GDI manipulates both sides of the injector. If you are only looking at one side, then you are not seeing the whole picture. Voltage is typically applied to a bank of injectors, and only one in that bank is activated on the other side. Therefore, you will see the voltage supply trace for the bank even when it's not that injectors turn to fire.
So...you see voltage pattern with no 'work' or current flowing.
Place channel A on the high side of the injector and B on the low side. Place the current probe on C. Make sure your channel grounds are on battery negative. Use attenuators on A and B. Now get plenty of capture time on the screen. Once you get a capture, use a math channel A minus B. This will show you the voltage drop across the injector.
When you examine the result it will all be clear to you.