Solution
In the ⋖ ⋗(Scene Intelligent Auto), ⋖
⋗(Portrait), or ⋖
⋗(Close-up)mode, the camera automatically judges the shooting environment to determine whether the built-in flash fires or not. Therefore, the built-in flash may automatically fire in low-light environments even if you do not want to use it.
To prevent the built-in flash from firing automatically, change the shooting mode.
For the details, see the built-in flash section at List of functions that can be set in each shooting mode (EOS REBEL T3i/EOS 600D).