Syncing issue between dynamic link with Adobe Premiere Pro and After Effects

If you play this video you'll it's not synced up like how it's meant to be

The reason I linked the Comp from AE to Premiere was to apply a Youtube Subscribe motion graphic I did that and chose to export it in Media encoder. And this is what came out. 

Next time should I just export comp into Premiere < get the subscribe button done, then bounce it back to avoid something like this? 

I will upload video of audio reacted content in a little bit to show you difference of what it looks like before YOUTBE Motion graphic was applied.