Camera target is off

Well…without seeing your blender file and your puzzles I can only provide you generic advice.

1. Dont use From Cursor.
2. In Blender select your camera, then from the View Menu (top menu of blender), select Cameras, then select Active Camera. If you only have one camera in your scene you can just press 0 on the number pad. This will show you what your camera is going to see when V3D starts unless you have animation or puzzles affecting it on load.
3. Recommendations: Place an empty at the position you want your camera to start, rename the empty. CAM_Start_Location. Create another empty at the location you want your camera to look at and name it CAM_Start_Target_Location.

In you initializing puzzles (the first few to execute), set an Set ActiveCamera puzzle and place your active camera object in it. Then place a TweenCamera to puzzle immediately following the SetActiveCamera Puzzle. Set the position of to CAM_Start_Location and the LookAt to CAM_Start_Target_Location, set the move to linear and the seconds to 0. This will ensure your camera in Blender is positioned precisely in V3D.

It appears you have four camera location empties.
This is what I believe is happening.

You start your scene at camera_initialize_start and looking at camera_initialize end.

For the sake of simplicity I am going to assign the z values to explain whats happening. They do not match what you have going on precisely.
Camera_initialize start is at z=5
Camera_initialize end is at z=.2
This sets the initial position of the camera and has a time value of 0.

When the user clicks on the eyes
The camera Jumps to (because the tween time is 0),
The camera moves from Camera initialize start to camera_tween_start.
Camera_tween_start is further away from the monkey…so we will say Z=6
The camera target changes too … its now camera_tween_end and its located closer to the monkey…lets just say z=.1

So you moved the camera further away from the monkey… the camera is moving backwards.
You also moved the target closer to the monkey which also adds to the effect of the camera moving backwards.

If you want the camera to move forward…. move the camera_tween_start somewhere closer to the monkey.

Recommendation: You named your initial empties correctly. But your other names may make the understanding of how this works more difficult.

You may want to rename Camera Tween Start to Camera Tween End. Its the location where the camera will end up when the tween is completed. You can leave the When clicked Tween camera look at to be the same as the initial Camera_initialize_end.

But again the naming is odd.

I would suggest renaming your emtpies:
Camera_initialize_start. >>> Camera_Start_Location
Camera_initialize_end >>> Camera Start_LookAt
Camera_Tween_Start >>> Camera_Tween_Location
Camera_Tween_End >>> Camera_Tween_LookAt

In the tween puzzle…the first object is the “position of” you want the camera to move to. The second position is the look at. This is where the camera is pointed to. The tween puzzle moves the camera from its current position to the position specified in the “position of” within the tween puzzle.

I think you may be confusing that the tween puzzle specifies where to start and where to end up. But its really move the camera from where its at…and. move it to the new location and look at the specified location. The seconds is the time that this will ocurr in…longer durations make the camera move smoothly.

Hope this helps.

just a little advice: never rotate cameras around its local Z axis. otherwize you will get the effect of a tilted head.