I think you're right. I was thinking the same thing. But, if this is the case, then I end up in a different theoretical problem.
The two bodies start out at relative rest in this frame and so there is a total of 0 momentum.
When the electromagnet starts to accelerate (from left to right) there is an increase in positive momentum.
And if momentum is always conserved, which it is, then there must be an equal offsetting increase in negative momentum (from right to left) at the same time.
But if there is a delay between when the permanent magnet starts to accelerate and when the electromagnet starts to accelerate then, as far as I can tell, momentum is then not conserved.
There seems to be a problem here, and that's why I posted this question.