Thank you leeastone! Yes, this is how jammr works.
You are also right that the server records the jam as shown in the first table.
It is hard for most people to think about how everyone hears a different time-shifted version of the jam. This is why I focus on explaining the two rules for playing in sync instead:
1. Play at the same tempo as jammr's BPM setting.
2. Make sure the BPI setting matches the length of the chord progression in beats.
Anyone following these two simple rules doesn't need to worry about understanding the details.
The details are interesting if you want to find cases where you can play in sync successfully without following these rules. There are exceptions to the rules although they are limited!
For example, if there are just two people in a jam and you don't care about the recording being in sync, then you can play alternating A and B intervals instead of just repeating the same A interval every time.
Or a saner example is that you can safely play a chord progression whose length is a divisor of the BPI. So if BPI is 32 then you can play a chord progression that is only 16 or 8 beats long and you'll stay in sync.
Usually it's best to stick to the rules though
Thanks again for sharing this. I'm sure it will help others understand how jammr works more deeply.