It should be properly flashed and you shouldn't have any exposed wood.

The wood is exposed when the old aluminum frame is removed but is covered by the new window frame. I wonder if we should put something like tar paper in between the wood and the new window? Thank you!

Honestly, yesthere should be something there, be it poly or I guess felt paper would work. I would be more concerned that the window head is flashed properly as that is the most vulnerable part.

I agree head flashing should always be done just because it doesn't add much cost...but did the contractor not do it because of the substantial overhang of the roof and the relative location of the tops of the windows to that? I doubt much water get's up that high.

I would use some good flashing tape, and do the corners very well.

caulking and your drip cap is you’re first line of defense, use a quality caulk and maintain it.

How about this one? No roof cover.

The window is Milgard Z-bar. The online installation video does show anything other than caulking. I wonder how it get waterproofed.

"I wonder how it get waterproofed."

Flashing tape and drip cap.

I don't have the picture that shows the exposed wood after removing the old window. A similar case I found online is shown below. The contractor put Milgard Zbar window directly on top of the exposed wood.