The problem is that your individual rasters are not aligned. So, when they are added the result is a weighted average for the values in the overlaping area. To solve this you have to use a merged vector layer whose extension must be used for producing individual raster. I used this procedure for testing it:

1) I created two vector layers where they are overlaped in some area:

![enter image description here][1]
  
2) I merged them and I wrote down its extension:

![enter image description here][2]

3) Using the extension to rasterize the first vector layer: 

![enter image description here][3]

4) First vector layer rasterized:

![enter image description here][4]

5) Second vector layer rasterized:

![enter image description here][5]

6) sum_raster obtained by using raster calculator. You can observe that the sum is 20 in overlaped areas (Value Tool plugin).

![enter image description here][6]


  [1]: https://i.sstatic.net/b97wm.png
  [2]: https://i.sstatic.net/ZolUG.png
  [3]: https://i.sstatic.net/0M592.png
  [4]: https://i.sstatic.net/R9z84.png
  [5]: https://i.sstatic.net/2dVs0.png
  [6]: https://i.sstatic.net/PsY7z.png