How to put a long picture overlay on top without imovie making the image scroll
This could be due to a variety of issues and due to lack of details I don't exactly know what the problem is. So, instead I am going to answer your original question: How to put a picture in picture without any animations?

I am assuming both footage are on the timeline properly. I will refer to the top one as footage x and the bottom one as footage y.



Select footage x
Select the second icon from the left in your effects toolbar (when you hover it should say "Video Overlay Settings") (I say second because, although not shown in the picture, there is a wand enhancer icon before it.)





Make sure Picture in Picture is selected and the transition time is set to 0

Select the crop button in your effects toolbar 

Ken Burns will most likely be selected and whats causing your issue. Switch this to Fit or if you need to Crop it set it to Crop to Fill 
Select Footage Y and repeat steps 4-5


This should create a picture in picture effect without transitions or zoom-ins.

Images and References:

https://support.apple.com/kb/PH22931?locale=en_US

https://support.apple.com/kb/PH22921?viewlocale=en_US&amp;locale=en_US