When should I deal fire damage to a creature trapped inside a burning web from the Web spell?

I have looked for this exact situation a lot already and don’t think it has been answered yet. I am a newer DM and think I know the rules fairly well, but if I am wrong and have debated with my group for nothing, please let me know.

We just had a session where our wizard cast web, and then lit portions of the web on fire to damage the creatures inside the web.

The web spell reads as follows:

The webs are flammable. Any 5-foot cube of webs exposed to fire burns away in 1 round, dealing 2d4 fire damage to any creature that starts its turn in the fire.

My group argued that because the creatures trapped in the web would be starting their turn in the flaming web, they should take 2d4 fire damage immediately (at the end of the wizard’s turn). I interpreted the description to mean that the damage would be dealt at the start of the creatures’ turns, as the spell says “2d4 fire damage to any creature that starts its turn in the fire.”

I tried to explain that it really doesn’t make a difference in this case, as no other creatures around them had any actions to save the creatures caught in the web, so whether the creatures took damage at the start of their turn or right at that moment, they would still be taking the damage before using their action. My players argued that it should happen right away since they wanted to know if the fire killed the creatures, or if they should keep attacking them.

Because I am playing with new players and we are only playing for the summer with the interns at our work, I try not to be a stickler for the rules in this mini campaign. I ended up saying we will let it happen right away (since it didn’t matter anyway), and I would look into it before our next session.

Reading the spell description again, I still think the damage should happen at the start of the trapped creatures’ turn. Any advice, insight, or links to helpful discussions would be appreciated!

TL;DR: If a creature is trapped inside a web (from the web spell) that is on fire, should that damage be rolled at the start of its turn, or right away?