608.2c The controller of the spell or ability follows its instructions in the order written. However, replacement effects may modify these actions. In some cases, later text on the card may modify the meaning of earlier text (for example, “Destroy target creature. It can’t be regenerated” or “Counter target spell. If that spell is countered this way, put it on top of its owner’s library instead of into its owner’s graveyard.”) Don’t just apply effects step by step without thinking in these cases—read the whole text and apply the rules of English to the text.
If it involved drawing multiple cards, that would happen one at a time.
121.2. Cards may only be drawn one at a time. If a player is instructed to draw multiple cards, that player performs that many individual card draws.
Some cards set up a repeated process. Such repetitions would obviously happen one at a time.
None of the above applies to Rionya, Fire Dancer. It's like a kicked Rite of Replication, which has an explicit ruling in Gatherer that the tokens arrive at the same time. Ask that other player if they have a source for their claim.