To share a video link that will begin playback at a specific point, all you need to do is add a bit of code to the end of the URL. Just add: #t= followed by the timecode of where you'd like playback to begin.
Here is an example where playback begins one minute and two seconds into the video: https://vimeo.com/81400335#t=1m2s
You can also use this parameter for embedded videos. To do this, simply add #t=(timestamp here) to the end of the player URL in your embed code. For example:
<iframe src="https://player.vimeo.com/video/81400335#t=1m2s" width="640" height="360" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>
If you're embedding a video and would like it to automatically start playing, you can add the ?autoplay=1 parameter before #t= as shown in this example:
<iframe src="https://player.vimeo.com/video/81400335?autoplay=1#t=1m2s" width="640" height="360" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>
Note: Unmuted autoplay is not supported in Chrome or Safari (desktop/mobile). If autoplay is blocked a browser or device, the viewer will be required to select play in order to begin playback at the specified timecode. Learn more here.