Whoops; you're right.
Must have had something on the tracks I tried previously because I verified it by looking at the Event list and it showed the audio starting at 1-1-0 (even though it visually looked like they started later).
This time is behaved as you stated.
Strange - it used to work the other way. If From-Thru is set to full track it should work.

The alternative is to use Track - Save Track to File, which asks if you want to include the silence at the beginning, and works as expected.

I do not work here, but the benefits are still awesome
Make your sound your own!