Judging by the demo footage, it just cancels the Dynamax altoghether.
Note that the rain would happen after the HydroPump (so it wouldn't get the effect on the go), same for all other conditions, meaning that they can very well be reacted to (or even predicted), without needing a reactive dynamax, but also allowing a reactive dynamax (you just set rain, i'll commit my dynamax to eat that rain boosted hydropump with my boosted HP and set sun instead)
Yes, weather wouldn't influence the first attack, but your post actually made me think about something hilarious when facing mons with fairly expanded movesets.
Fight against Raid Tyranitar:
Sandstorm kicks in!
Player: "Ok gonna use a Water attack, Sobble evolution!"
Tyranitar used Max Flare (Fire Punch) on your partner's Grookey evolution! Grookey evolution is at 25% HP.
Sun kicks in!
"Ok, a neutral attack against Tyranitar's boosted 100+50%/100 bulk didn't do much."
Partner 1: "Grookey evolution, your Solarbeam in harsh sunlight!"
Tyranitar used Max Stone (Stone Edge) against Partner 2's Scorbunny evolution! Partner 2's Scorbunny evolution is exhausted!
Sandstorm kicks in again!
Partner 1:"Well, here goes Solarbeam. Can you use a water attack again?"
Player: "What if he uses Max Flare again? You're going to be food for Korviknight and he's still at 70%, we're not even at the shield yet and one of us is already down"
Partner 3: "Let's neutralize him and focus on damage later. Come on, let me try a status move. After all, I'm the loser without a starter, I'll leave damage to the two of you. Going to use my Gengar (we've seen Haunter popping up in Wild Areas) to put it to sleep with Hypnosis so we can focus on damage."
Tyranitar used Max Electric (Thunder Punch) on Player's Sobble evolution! Player's Sobble evolution is exhausted!
Electric Terrain kicks in! Tyranitar cannot be put to sleep!
Partner 3: *looks at partner 1*....
Partner 1: "Don't look at me, I'm still waiting on my Solarbeam here and I'm gonna be dead next turn probably. I'm sure Gengar will fare fantastic against a Tyranitar with Sandstorm up. Hey, we still haven't sustained its Dark STAB attack, I'm sure Gengar will. Hey, don't you happen to have Focus Blast on it, do you? That's a 100% reliable move!"