That move is NOT legal.
All Combat Movement is simultaneous. The ships for the Amphib moved in at the same time the aircraft flew over to attack the SUBs. So ALL of the ships and aircraft were in the sea zone (and subject to attack and defense rolls) when the SUBs were attacked.
Also, since you DID have SUBs there, the Battleships MUST attack the SUBs, they cannot hold back to fire their support shots for the Amphib. The Sea Battle engages first, so the BB’s fire there and cannot fire again.
What you opponent did in the last game was violate the core rules of the game in terms of the sequence of a move. First you do ALL Combat Movement, then ALL COMBAT, then all Non-Combat Movement. Your opponent did a Combat Move, then rolled Combat, THEN did ANOTHER Combat move after the first combat was resolved, then did another Combat.
What he did is no different than sending INF and FIGs to attack, as an example, Ukraine. Then after you win that battle sending your tanks through Ukraine to attack Caucuses.
There are very specific and explicit rules for doing an Amphib assault, and your opponent violated them.
What SHOULD have happened was all of the ships and all of the aircraft enter the sea zone with your SUBs. Your SUBs would get to fire their opening fire. All of his naval units and FIGs could then fire on your SUBs. Any that lived through that could then either submerge or they could continue to fight. Once that is resolved, then and ONLY then do the Transports offload the the attack on Western could take place, without BB fire, or the support of any of the units that participated in the naval combat.