About the warsong commander and charge interaction, it depends on the order of your play (you can try it yourself).
If you play the warsong commander last, it will gives the given-charge-minion +1 attack. If you play warsong commander before the charge spell, it will not.
So I will assume, from the coding side, it happens because the re-evaluation order of the effect type. Aura effect (warsong) is re-evaluated everytime new effect added to the board just before that new effect added. So warsong will not buff the minion that given charge after warsong already played. Even southsea deckhand won't get the buff if you play it after warsong, but will get the buff if you play it before warsong. Yeah I know it's weird and might categorized as a bug.
About the etc, the effect is evaluated when a minion attack, it's not Aura like warsong, so compare it with warsong isn't exactly right.
The right comparation is Magic Carpet.
The text is "After you summon 1-cost minion", yet it still trigger the effect if you play the reduced Sea Giant to 1 cost. It doesn't need to say "After you summon minion with 1-cost". Both are interacted with things minion do on the board.