I like to tap the "C" key which allows me to cycle thru more intuitive Camera controls (with the mouse)  the the Rotate XYZ options in the Cam Transform area.

Go to the beginning of your timeline. Reveal all the Camera Transform  options. Turn on Keyframes for them all (just in case)

Move your timeline to a point where you want to Move Up and Tilt Down. Tap "C" and use the interactive mouse controls to pose the Cam. Since all attributes are already keyframed, they will be automatically created when you position the Cam with the mouse controls.

Good point Fuzzy.

With a 2-node camera, the camera ALWAYS faces the Point Of Interest (POI). 

The camera Position is the space the camera sits in the "world". 

The POI is the point within that "world" that the camera lens is pointing to.

If you move the POI downward in Y space, the camera will effectively rotate downward to follow it - but that rotation will not be represented in the camera's rotation parameters.  The camera's rotation parameters wil be ADDED to whatever the POI forces the camera to do.

If the camera passes the POI in Z space, the camera instantly flips so that it is still oriented towards the POI.  If the POI is confusing you, just switch it off in Auto Orientation settings and work with a one node camera until you get the hang of it.

When doing complex moves with AE's 3-D camera I always put my camera on a dolly. I also attach the point of interest to another null. This makes complex moves much easier. It also provides a way to easily animate the focus and the point the camera directly at what you want to point ot at by animating the position of the POI null.

Here's a screenshot of a simple timeline setup. The two 3D nulls are named Dolly (at the camera position) and POI (for point of interest)

Here is the animation preset that I use to tie the camera's point of interest and focus distance to the POI null. The expressions work with or without parenting.

The camera Point of Interest expression:

poi = thisComp.layer("POI");
fromWorld(poi.toWorld(position))

The camera Focus Distance expression:

C = thisLayer;
POI = thisComp.layer("POI");
cp = fromWorld(C.toWorld([0,0,0]));
fp = fromWorld(POI.toWorld(position));
length(cp, fp)

This technique makes animating a camera a lot easier.