In this case, the second is correct. "Tight" is a resultative adjective that refers to the final state of the tin.
You did not close the tin (to be) tight.
You did not close the tin tight (enough).
New Oxford American Dictionary
• (of a ship, building, or object) well sealed against something such as water or air:
[in combination] : a light-tight container.
More information here about resultative adjectives: