Does Star Springs effect get put on the stack?

Yes, the ability of Star Spring is placed on the chain (often referred to in other games as the "stack") when its trigger condition is met.

According to the Showdown Flow and the Chain Rules in Riftbound:

1. Triggering: When you play a non-token unit to the battlefield where Star Spring is located, the ability triggers.
2. Chain Placement: Because this is a triggered ability, it is placed onto the chain.
3. Optionality: Per RiftJudge FAQ #10264, since the text says "you may," you are not required to trigger the ability. If you choose to use it, you place it on the chain at that time.
4. Reaction: Because triggered abilities use the chain, both players have an opportunity to play [REACTION] cards in response to the Star Spring ability once it has been placed on the chain (as the chain is now in a "Closed State").
5. Resolution: The ability resolves in a Last-In-First-Out (LIFO) manner along with other items on the chain.