How far someone is offside isn't irrelevant, neither is the fact it's more than 1 player. If a player is 6 inches offside it's highly unlikely it'll be seen by the ref or touch judge.
If, like Percival & Makinson were for instance, however a player is 2/3/4 yards offside and in line with the play the ball then it's likely to get pulled.
Also you can be involved in play even if you don't make contact with the ball carrier. If you're offside and advance toward the attacking line then you're likely to get penalised, especially if the attack don't gain any particular advantage.
Saints lost it in that period. They were yards offside time after time on their own line. The fact they didn't adapt after the first couple of penalties shows they weren't thinking. As evidenced by Percival? getting pinged for offside (proven to be correct by the video), whinging about it to the ref and then being offside again from the following penalty.
Saints were yards offside. Don't blame the ref, blame your players for not using their heads.