The directions that come with your tension gauge tell you to test with the thread through the eye of the needle.
I do know that lower, and more accurate readings will be obtained with the thread NOT going thru the eye. Needle eyes can have different sizes and even shape, dependant upon the size, brand, (style such as ball point -vs- semi-ballpoint-vs- sharp) and finish of the needle. Also, the angle and direction you pull at through a threaded needle can be very critical, which can result in problems getting repeatable readings, especially on some types, brands, and colours of thread.
It is more important to get the bobbin tension set correctly, since you are really only setting the top tensions up "in the ballpark", and you have done an "H" or "O" test design to make sure 1/3 of the thread on the back is bobbin thread.