Yesterday, I asked a question regarding the spell Sickening Radiance. The most upvoted answer satisfied the question, but it also added this small line:

Yes, forcefully moving enemies into the area does cause them to be affected by the spell.

Note, however, that in that case they would not also be affected on their turn. Sorry, no 8d10 damage per round here...

I don't see anything that would make this the case, yet it is upvoted (as of writing) five times, hence this question.

Sickening Radiance states:

When a creature moves into the spell's area for the first time on a turn or starts its turn there, that creature must succeed on a Constitution saving throw or take 4d10 radiant damage [...]

As far as my understanding goes, a turn and a round are two explicitly defined different things by the PHB:

The game organizes the chaos of combat into a cycle of rounds and turns. A round represents about 6 seconds in the game world. During a round, each participant in a battle takes a turn. (PHB, 189)

So, to give an exact example, let's say an enemy is pushed into Sickening Radiance and is affected by the spell ("moves into the spell's area of the first time on a turn"). If during the same round, the enemy's turn starts inside of it ("or starts its turn there"), are they affected again?