When a player tucks a card for income, they "also gain that resource immediately" (page 28, Rules Reminders). The rulebook does not explicitly define whether this immediate gain is part of the free action or a separate event for the purposes of other triggered effects.

However, the context on page 28 presents the immediate gain as a direct consequence of the tucking action:

• "When you tuck a card for income, you also gain that resource immediately."

There is no mention of this being a separate event or triggering additional effects beyond the resource gain itself. The rulebook does not provide any rules or examples of triggered effects that would distinguish between the tucking and the resource gain as separate events.

Summary

Based on the rulebook, tucking a card for income and immediately gaining the resource are treated as a single, unified action. There is no indication that the resource gain is a separate event for the purposes of other triggered effects.

Source: page 28, Rules Reminders
If you need to know how this interacts with specific triggered effects, the rulebook would need to define such effects or provide examples, which it does not.

Source: Core Rulebook (pp. 15, 18, 19, 28, 7)