I think outsiders are like "Deus-ex-machina", the "God outside of the machine/System", able to bypass Common rules of the universe.
The Tower likely has a set of rules that enable It to be all that It is, like a Spell. Just like HxH nen, you get something in Exchange for a New rule added. My take on this is that whoever made the Tower wanted something that reality couldn't give by itself as It were. So this person created a confined space with rules in Exchange for Powers that didn't exist before. Namely, inside the Tower things would be able to happen that would be Impossible outside.
Regulars are born within the Tower, and thus they are also bound by the Tower's balance, they gain nothing extra because they can get the bonus but are confined to these rules as well. Irregulars on the other hand can challenge the Tower to get its benefits while not being held by their rules. They only have to complete its rites (tests) in order to access whatever It is that the Tower can Grant you. The higher the difficulties, the higher the rewards.
So imo Bam is a different kind of irregular because he was first born within the Tower, and then considered dead and reborn outside. His birth was limited to the Tower's reality, but he broke Free from these limits afterwards. Hence his Power is growing fast despite having a low starting point. Mazino on the other hand was powerful since the beggining, he was, like his bug, beyond the reality's limits, and could never be born from the Tower as such.