Posterize time question

Comp Framerate affects all layers in the comp. The PosterizeTime effect only affects the layer it is applied to. And then, there is PosterizeTime, the Expression Method which only affects the property it is applied to. HTH.

You have a couple of options but before I explain them let's talk about frame rates for footage and for compositions.

The frame rate of the footage determines how long it takes to playback the footage and it does not matter what the comp frame rate. Changing the comp frame rate does not change the time it takes footage to playback. Changing the interpreted frame rate of footage does change the time required to playback the footage.  Let me give an example. If you have some footage shot at 120 fps then 10 seconds of that footage will take 10 seconds to playback no matter what the frame rate of the comp is. Drop the footage in a comp set to 30 fps and every 4th frame will playback. Drop it in a comp that is 240 fps and each frame will be shown twice. When the frame rate of the footage is different than the frame rate of the comp you have several blending options to try and make the footage look better. 

If you want the footage to slow down you have two options. The first is to use Time Remapping, Stretch, or several of the other time tools available in AE or from third-party developers. The second option is to change the interpreted frame rate of the footage in the Project Panel.  Personally I usually change the frame rate interpretation.

If you nest a comp or pre-compose some layers and the nested comp's frame rate is different than the main comp's frame rate, the Main comp's frame rate will be used by default. Let's say you have a comp with some animation that is 15 fps and you drop that in a comp that is 30 fps. Ten seconds in the nested comp will still be 10 seconds in the main comp, but if you have animated the position of a layer in the nested comp so that it moves 2 pixels per frame in the nested comp when you check the animation in the Main Comp you will find that the animated layer moves 1 pixel per frame. This confuses a lot of people until they realize that animation is based on time, not on frames. 

There is an option to Preserve frame rate when nested or in the render cue. You'll find it in the Advanced settings. Turn that on drop your 8fps comp in a 24 fps comp and you will get the kind of motion you without posterize time.  If you do not turn on those settings and you send the 8fps comp to the render cue and you choose to render at 24 then you will lose the 3 repeated frames and your animation will smooth out.  If you use the Adobe Media Encoder you have to be very careful with the FPS settings because you can really get things screwed up including the timing. 

Now that I have said all that, if you want to deliver an 8fps animation as a 24fps video repeating every frame 3 times then the two easy options are set up a 24 fps comp and use Posterize time or set your 8fps comp to Preserve frame rate and then nest it in a 24fps comp and render to a suitable delivery format making sure that the frame rate is correct in the render settings.

Using Posterise Time allows you to easily work and export a comp at 24 fps while still retaining the stop motion look you want. They both achieve the same effect when you're working, it's really when you're exporting that using PT will help you keep your export process easy.