Each participant should wait until their own tracks have finished uploading before closing the Zencastr tab.
As soon as the uploads complete each participant will receive a pop-up message on your screen saying "All your tracks have finished uploading and it is now safe to close the tab."
Each participant need only wait until their tracks are finished. If one participant's uploads are taking longer, the other participants don't need to wait as long as their own uploads are complete.
Mp3 tracks generally finish almost instantaneously once the recording is finished since they are uploaded as you record. Wav tracks do not begin until the Mp3 upload has completed and can take a bit longer. Generally five minutes or so but it is dependent on the internet connection. If your guest cannot wait around for the wav upload, they can leave early as long as the Mp3 has completed and you are ok with only having a Mp3 track for this recording.
If the guest accidentally leaves early, you can help them retry the uploads by following the instructions here: One of the Tracks Didn't Finish Uploading, How Can I Recover it?