Who is in the wrong?

No one should have gone back to their desks - the source of the fire needs to be confirmed, not just by people assuming that’s what it was. There are procedures to follow, buildings cleared etc.

If it's a small building I don't see the point of proceeding to the fire assembly point to be fair. Surely the point of the fire assembly point is to vacate the building so the fire hazard can be dealt with before giving everyone the go ahead to come back in, if it was dealt with fully on the way out and literally everyone in the small building new that and there was no other risk then there was no point going outside surely?

Everyone should follow evacuation procedures. Just because one cause of fire was found, doesn't mean there isn't a secondary fire in the building. I am sure there is a clear evacuation policy that states that everyone should meet the fire warden at a designated spot and not to return to their desks until given all clear.
If the people proceeding to the meeting point were reprimanded, I would report whoever did the reprimanding to the fire officer as they clearly need more training.

If the alarm goes off, you have to go outside. Even if you know what it is and know the place is safe. In your own home, you can just stay inside but in work, you have to leave until the building is cleared as safe to go back in. Because if you stay and anything did happen, your employer will have to make
massive payouts. So yes, you’re unreasonable to stay and will be reprimanded. In this case, you knew it was safe but what if it was an electrical fire and someone unplugged whatever it was and everyone thought that it was safe but there was actually a fire inside the wall, spreading? And you all just go sit back at your desks?

Nope, if an alarm goes off you have to go
outside until cleared to go back.

I'm actually going to guess that the ones who carried on outside were reprimanded. They were definitely right to do so, but I can imagine some managers being annoyed and seeing it as a waste of time and thinking that as the (potential) cause had been found that it was unnecessary to still go out

No idea which one was reprimanded, but the staff who continued to the fire assembly area were following the correct procedure for a fire alarm. The staff who went back to their desks were not.

If there's an evacuation due to a fire alarm, you go to the assembly point even if you think there is no danger, unless a fire marshall actually tells you to return to your desk.

So if anyone was told off, it should have been the staff who returned to their desks.

The ones who went back in because health and safety is ridiculously uptight. Even though the source was sorted out🙄

The ones that were reprimanded were probably the ones that went back to their desks.

I think it's reasonable-ish because until they get an all clear, they can't know for sure that there isn't something else going on elsewhere.

The ones who didn’t walk outside were reprimanded?