The trick is you need to make sure all of the tilemap that you want to paste is onscreen before pasting.
For everything else the usual method of using paster as a screen is to
1. move paster to the location
2. paste objects
3. move paster back to original location
For the tilemap or even particle object you need to move both onscreen.
1. move tilemap to the negative of the location you want to draw. (-x,-y)
2. move paster to the top-left of the screen
3. paste tilemap
4. move paster back to original location
5. move tilemap back to (0,0)
The above will work as long as the paster object's size is less than or equal to the screen size. If it's bigger then you'll need to scale the layout or layer so tha everything is on screen before pasting.