Normalize Chain different from Normalize effect

I’m not sure why exactly, but applying Normalize in a chain is producing a very different waveform from applying Normalize in audacity.
This shows the results. Top is original .mp3, middle is normalized in audacity (-16db, apply offset=1/yes), the last clip is the result of the same normalize parameters applied in a chain.

The sound itself seems to be offset by .05 seconds.

Wondering what the problem is here exactly and how to fix it?

I’m guessing that the offset is because you exported as MP3. Did you?
MP3 always has a bit of padding at the beginning - it’s a limitation of the MP3 format.