Using the web interface with SpeedGrader, if you select a tool from the top and move the cursor down until it crosses into the document render area, you will notice that your cursor only appears on the document once it has passed enough space to accommodate the new origin for the selected tool icon. The mouse cursor origin is the top left of the icon. If you switch to say the writing pen which has an icon origin of the bottom left, you will notice a gap of about 10 pixels from where your cursor is and the actual place that the writing is appearing. It is probably easier to see in a video SpeedGrader - YouTube
Contrast the writing tool with the comment tool which has an origin of the center of the icon, and you will see that you can never write at the top of the page but you can place a comment at the top of the page.
Because of the difference in tool origins, you end up with handwritten notes that drift further and further down the page when using a touch monitor. The touch monitor is not the problem, you can see this problem clearly with just a normal mouse and monitor but, because you expect to write where you touch with a touch monitor, the issue becomes more apparent with a touch monitor.
Please make all the icons have the same origin.