I was told to do similar actions to mass confrontation like this - take a step back and note everything that's happening, let it calm down before involving yourself (the last thing you want is the 22 players turning on you).
Is this incorrect?
Depends on how proactive you class yourself as a referee, or in some cases, how brave you are. I believe the "English" way is to stand back and observe then take action but, in Scotland, officials would have been in, least 1, possibly 2, trying to act as barrier, separate who you can, yes, create that triangle view point but, I suppose its just what you feel comfy with
Also forgive me if this is stupid, shouldn't literally all the subs who came on have been cautioned too?
By LOTG you can yes, but, if you are going to caution for "entering field without permission" then, lets hope in the interests of making sure offenders are dealt with, that you catch ALL who are guilty of Violent Conduct, or, Adopting Aggressive Attitude or anything else Can you imagine yellowing carding 4/5/6 players and they go why and you go " cos you were on the park", yet you have missed 4/5/6 players who are guilty of violence or aggression? You would need to also make sure you catch ALL the subs who were on the park or else you are open to "well he was on also and you never cautioned him". Subs just being there, in that situation, no, course they should not be, but its a very low priority, if they were involved in a punch or so, then yes by all means make sure they got a red card. Its the sort of situation you wont know how you will handle it until it happens, how many folk will be involved, where on the park will it be, what will spark it, too many variables to discuss at length until it actually happens.
I think you have made a good example there of the difference between knowing the LOTG and knowing how to manage a game....two very different things...