Obviously without a recording or stat's for your SEE and the enemy Ezra/JML I can't verify but I have a feeling it's not that they took 5 turns in a row and it's simply that it looks like they did. I'm assuming the following:
1.) Ezra has reached full Purrgil stacks so anytime he performs an ability (aka even his basic when called to assist) he calls another ally to assist. Because Cal was down, the only person he could call is JML
2.) JML actually used his ult in the middle of his supposed 5 attacks (or you're counting the use of his Ult as turn 1).
3.) Between Ezra and JML Ezra has a bonus of 100 (60 from Ezra himself, 40 from JML) speed and could either gain an addition 20 permanently from Cal dying or speed up (+25%) from using a basic from the orange datacron. Ezra's base speed is 195. Add in good speed from mods of say 150 then that gets a total speed of somewhere around 345 prio to datacrons getting to 360 with the +20 or 431 (could get as high as 495 I believe with perfect speed on a speed set) with the speed up on basic which puts his speed on par to most GLs so it's not out of the question that he could potentially attack twice before your SEE depending on the speed of your SEE in comparison and how much turn meter you had when he took a turn. Also keep in mind, the bonus from the datacron to speed would also be applied to their JML as well.
If these three points are true, then the order of attacks from JML would be:
1.) JML uses Inherited teachings calling Ezra to assist who calls JML to assist him assisting (attacks 1 and 2 for JML)
2.) Ezra uses Kanan's Legacy to give JML a bonus turn (because it's a bonus turn and not turn meter, it's not blocked by SEE)
3.) JML goes into Ult, resetting all cooldowns, then uses Inherited Teachings again calling Ezra who calls JML (attacks 3 and 4)
4.) Ezra uses Kanan's Legacy again to give JML another turn
5.) JML uses one of their abilities (attack 5)
6.) Depending on speed disparity (JML is already 11 speed faster by base and gains an additional 40 from his leadership, though this would be countered by SEEs +40 of course, and possibly +25% from the datacron) between their JML and your SEE, they could even take another turn here for attack 6.
I haven't encountered Ezra/Exiled yet so I'm wondering if Exiled maybe has a similar issue that Damage Immunity has where some characters will pause before doing damage/attacking. If it does, this would also explain why you weren't seeing JML assisting as being an assist and is instead as if it was it's own attack because of the slight delay making it look even worse than you'd assume.
Capital Games Team