It's not necessarily a result of lag. The most prominent reason, assuming you don't have lag is chase chain. The server waits for a VERY short amount of time for chase to resolve, yet some chase chain can take quite a while. So after the chase finishes, you end up being behind.

And of course, lag is a thing. It can be either a network lag OR your computer not keeping up with the animation speed so everything is displayed slower than the server think it does, much like the chase thing. Except the chase thing is the game's fault (in term of design) whereas hardware issue is your fault.

But in any case, once you fall out of sync, It's very hard to catch up (thou on 1x speed you could catch up some). And as chase chain usually happen at beginning of a round via mystery, by the time you get to your 2nd move or something in normal attack order, it's likely that you are already far behind and the turn have ended.

Do note that "Position 2 just attacked" is meaningless in this regard, you really need to measure just what % of the round have already passed, taking into account of chase and mystery.

Whether or not the mystery "works right" depend on when the lag or dysync occurs. If it occurs BEFORE the cast (i.e. for example the enemy already triggered a chase chain with a normal attack BEFORE trying to cast mystery), then it would not work. Otherwise, if there was no "clutter" before, it would work.

Assuming no lag on either side due to network or hardware, there is nothing random about it, it's deterministic.

As for actual system lag, yes the game waits at end of round for the slower player. But as the slower player, you would not see the wait, because by the time you see end of turn, the game have already waited. And in case of dysync caused by chase, in reality the game have already waited for BOTH players. Note that the server does NOT keep in pace with the faster player, it can be even faster than the faster player.