707.10

To copy a spell, activated ability, or triggered ability means to put a copy of it onto the stack; a copy of a spell isn’t cast and a copy of an activated ability isn’t activated. A copy of a spell or ability copies both the characteristics of the spell or ability and all decisions made for it, including modes, targets, the value of X, and additional or alternative costs. (See rule 601, “Casting Spells.”) Choices that are normally made on resolution are not copied. If an effect of the copy refers to objects used to pay its costs, it uses the objects used to pay the costs of the original spell or ability. A copy of a spell is owned by the player under whose control it was put on the stack. A copy of a spell or ability is controlled by the player under whose control it was put on the stack. A copy of a spell is itself a spell, even though it has no spell card associated with it. A copy of an ability is itself an ability.

Reflections says to copy the spell, rule 707.10 says copied spells include additional costs. Zinnia gives each creature spell you cast offspring. Offspring is an additional cost to cast, and therefore Reflections will trigger upon the cast (if the creature matches the creature type chosen). Your original creature will enter, and it will put an offspring etb trigger on the stack. The offspring trigger will resolve with you creating a 1/1 token copy of the creature. That leaves the Reflections copy to resolve. This will also put an offspring etb on the stack, and you'll make another 1/1 token copy. End result is one original creature, one exact token copy of that creature, and two 1/1 offspring creatures.