I know ZIP about jumping (horsie picks up feet & goes over big thing, I hold on), but I do lunge my horse in side reins. Caveat is that you shouldn't do it for long periods of time & they can't be cranked tight.
Everything I do know about side reins tell me jumping in them is a bad idea.
How is the horse supposed to use his head and neck over the jump with side reins? He can't, not without punishing his mouth! So no side reins over fences.
I do longe in them, attached to a surcingle that has dees in the correct places. I use the side reins with elastic inserts. However, the horse only goes around on the flat, I don't longe a horse over fences in side reins either.
Lunging in side reins- yes - although I have never seen any without a donut or some elastic for give. Without donut / elastic, I think it would teach the horse to go behind the vertical because the reins wouldn't follow, he'd be bumped in the mouth.
Jumping in side reins, absolutely NO in my opinion. All that would teach a horse is poor form and to not bascule correctly as there would be no release. Worst case scenario would be injury if the horse tripped on landing, as the side reins would prevent the horse from using his head/ neck to balance.
If I were you and this is your trainer, ask what the purpose is (and take any response with a grain of salt). I would run, not walk to the nearest exit.
I'd think it would still be difficult to jump in side reins - even if the horse is still on the long line. I could see it if they were tiny jumps (which it sounds like they are) but he can't reach properly to jump in them. Also depends on the size of the horse - if it was a tiny pony, that'd be way too high for using side reins - on a 17-18hh wonder horse who can step over 2ft? Probably wouldn't recommend, but it might not interfere with the horse much.
I do understand the idea behind it that you want him to be nice and round and move from the hind end the entire time, not just on the flat.
I started taking lessons from a German girl who is mainly dressage. She doesn't understand why H/Js ever long on a regular long line and not in side reins all the time. Is the trainer primarily dressage?
Where am I and what am I doing in this handbasket?
It's not something I have ever found occasion to do (or recommend), but I don't know if there is enough information to comment intelligently in this case - how loose or tight were the side reins? Where were they attached? Since it was a flower box, were they cantering or trotting it, because it could be treated like a caveletti, in which case, plenty of people who wouldn't dream of jumping in sidereins are fine with them as caveletti work... And last but not least, was there a specific reason and what was it?
So in general, no, but there's not enough info here to say if this qualifies as an "in general" moment.
Your crazy is showing. You might want to tuck that back in.