Hi @Ali Hakimov,
A couple of things that may be messing with your intended results... Media Replacement controls do not support Time Remapping, Time-based effects, and Trimming. They cannot be translated over to Premiere Pro. You should have seen this warning when you exported the Mogrt from After Effects.
When you create a Media Replacement Control in AE, you are basically creating a container for new media to fill it in-- like an ice cube tray. The Dimensions, Duration, and Frame Rate for this container are defined by the media or comp you used to create the control. They are set and that's all that Premiere "sees" about this control once you are in Premiere. The caveat to this is that you can create Protected Regions on the Primary Comp which will enable Responsive Design Time. This will allow you to stretch or shrink your Mogrt in Premiere and will essentially make the duration of that media container longer or shorter. It will not speed up or slow down the footage though. As I mentioned above, Trimmed Layers are not seen in Premiere, but In Points are. So if you stagger the In-Point of the media you are using to make a Media Replacement Control in After Effects, this will be respected in Premiere Pro.
 
So in this example above... I will make all of these Media Replacement Controls in AE. Layer 1 control will start at 0:00 Layer 2 control will start at 3:00 Layer 3 control will start at 4:09
Those In-Points will be respected in Premiere Pro. Another trick: Double-click on the Media Replacement control in Premiere Pro to open up the secret timeline for that replaced clip. (I know! why is it secret?!?) Here you can do all kinds of things, like add effects, do speed ramp changes, even add multiple clips. It's another timeline.
 
The part of the timeline without the danger stripes shows you how much time you have to fill with your new clip and also shows you when the clip's In-Point is -- in this case it is 10 seconds into the Mogrt and not at 0:00 because the In-Point in After Effects is 10:00
 
You will see the last frame freeze if the clip is too short to fill the duration of the Media Replacement Control. Open the hidden timeline and move the clip into the active region / non-danger-striped area.
Hope this helps give some more context and tools to help you understand and work within the design limitations of the feature.
Cheers,
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