Day for starry Night Sky replacement.

It would really help to see the original shot. You need to do a lot of work on the skyline matte. I see you have used camera tracking but that isn't going to really help with the sky because it is so far from the foreground elements. 

The first step is to generate some kind of a matte to knock out the sky. The second step is to create a big enough star field to cover any camera movement. There will be a parallax shift between the foreground elements like the Joshua trees so stars will seem to move in relation to the trees as the camera moves, but Camera Tracking is not going to give you a surface that is far enough behind the plane of the trees to do you any good. The best option may be to set up a good procedural matte to knock out the sky from a copy of the original footage, then combine that with a gradient layer to fade the stars out as they approach the horizon and put that arrangement above the color corrected day for night footage.

If the camera move is not perfectly smooth you may have to motion stabilize the footage, add in the starfield that has been masked, animate the position of the stars a bit to give the parallax shift, then put the motion back in the scene using a null, parenting, and a couple of expressions.

If I could see the original footage I could give you a better idea of how to pull this off. The biggest problem I see with your screenshots is the lack of a decent matte to remove the sky and a gradient to fade out the stars. You need to create a nested comp (pre-comp) like this to use as a luma track matte for the star layer. 

The first thing I did was draw a couple of masks on the footage layer so I could use Keylight to make the horizon transparent. Then I added a black solid below the footage to fill in black below the horizon and copied the bigger mask, the brown one with the add mode to the black solid and changed it to subtract. Then below the whole thing, I added a gradient shape layer to give me a black to white gradient above the horizon. 

This comp can be nested in the original comp and used as a Luma track matte for the star layer. That comp would look like this:

I just used a NASA photo of the Milky Way.  The last step would be to animate the position of the Milky Way layer to give you the parallax shift and movement you need. I can't tell you the most efficient way to do that without seeing the original footage, but, once again, I don't think camera tracking is the right tool for that. That composite would look a lot better if the foreground was not covered with your original starfield.

You need to apply some feathering or a gradient matte to your star element (or to the cutaway of your footage) to create that falloff that you're looking for, and if that nice gradiated color isn't present in your footage, you'll need to recreate that as well. There are a couple different ways to do this, which will probably all end up with similar-looking results. 

Assuming the sky color gradient exists in the footage, can add a mask (heavily feathered) to the stars layer itself, and just lay that on top of the footage. If the stars layer doesn't already have transparency (where the stars aren't), you could use the Add or Lighten blending mode to composite the stars on top of your footage. Adjust the layer's Opacity and your mask feathering until you get the desired look.

If there are objects like the tree that extend beyond the "barrier" you're creating here, you could handle those on a case-by-case basis, using a strategy similar to what you've tried above. Duplicate your footage layer, trim to the range where that object is visible, extract it using effects, and then add it back (above the stars) using the Multiply blending mode, which will help any light-colored edges disappear. The stars will then be sandwiched in between the original footage (below) and anything that needs to overlap them (above).

If the original footage doesn't have that nice gradient in the sky, you'll need to create that using a similar strategy. Create a Solid comp-sized shape layer in the dark blue color you're after, then use a heavily-feathered mask and blending modes to get the look you're after. You could also do something similar using color correction effects, on a masked Adjustment Layer, or using the effect compositing options on a layer mask.

You could achieve something very similar using a black/white gradient as a matte layer for the elements above, but that may introduce some extra complexity you may not be looking for here. If you're finding the masks aren't a good solution because of the movement of the shot, mattes may be the better choice here. Without seeing the shot itself, it's difficult to make a good recommendation on that.

Let us know if you need additional explanation on these. Good luck!