During stringing, a calibrated string machine pulls the strings with a preset tension. However, this tension is NOT the same as the tension in the finished racquet, not even directly after stringing. RacquetTune measures the string tension in the FINISHED RACQUET, not the setup tension indicated by the machine. The discrepancy between these two values depends on several factors, all of which influence the tension substantially during stringing:
Creep/stress relaxation. All strings experience deformation leading to tension loss over time. This process is initiated immediately following clamping of the strings. The degree of tension loss varies with the material of the string – polyester tends to lose the most – and the effect is enhanced by high temperatures. Within 30 min, the strings may have lost 2-6 kg of tension. 
Clamp motion. Theoretically, this could both increase and decrease tension, but clamp movement usually results in a reduction. A 1 mm motion in the clamps can change the tension by up to 2 kg. 
Frame distortion. Due to the forces applied during stringing, the racquet frame is deformed; to which degree depends on the type of racquet and the string machine support. Again, a 1 mm deformation is equal to a 2 kg tension loss. 
Friction. When pulling the crosses, the friction from the mains causes the tension on the opposite side of the racquet to be much lower than the preset stringing tension. Upon completion, the tension difference in the stringbed is evened out, resulting in an overall lower tension in the crosses than in the mains. This effect accounts for a loss of 1-3 kg in the crosses. 
Elongation in the mains. Pulling the crosses over and under the mains causes the mains to change shape, from straight to “wavy”, which results in an elongation of approximately 0.5%. This equals a tension increase of roughly 2-5 kg. 
String machine type. Constant-pull machines usually maintains the indicated load for a longer period of time than lock-out machines, thus adjusting for some of the creep and resulting in a higher stringbed tension.
String tie-off. There is a small tension loss when the strings are tied off.
References, calculations and more details for the points above
 This is a property of all materials, especially polymers. An example of tennis strings is shown below (reference)
 and  The relation between strain and stress is: σ = ε*E Assume a 300 mm long string with diameter of 1.25 mm and a Young modulus (E) of 5 000 N/mm^2. Since stress is tension over cross section area and strain is relative elongation, the tension change in 1 mm elongation is:
T = π*0.62^2*5000*1/300 = 20 N (or 2 kg)
 The value taken from Cross & Bower who measured each string with load cells during stringing.
 The figure below shows a crude model of the main strings. D is the string diameter and L the distance between the strings. If you look at a piece of of the main it goes from being L long to being √(D²+L²) (Pythagoras). This means that the strain (elongation over length) can be approximated to 0.5*(D/L)². For most racquets D/L is about 1/10. Which using the same calculations as above leads to:
T = π*0.62²*5000*0.5*(1/10)² = 30 N (or 3 kg)
A good illustration of the combined effects of creep, frame deformation och string elongation is the measurement on the middle main string done by Love and presented below (reference).
This test was also repeated with the set up described on the previous page. The effect was here even more dramatic with the tension dropping to half the set value before increasing again:
The explanation for this behaviour is that the tension initially drops due to creep/stress relaxation in the strings and deformation of the racquet head. There is some jaggedness in the curve due to pulling and releasing strings. Then the tension starts to build up again when the crosses are pulled and the mains gets longer due to their wavy form. The racquet head deformation is also restored, which further increases the tension. It can be noted that the curve goes up stepwise for each new string. The final tension is close to the initial one, which of course is a coincidence (it could end up both lower and higher than the initial tension).
Two things to notice: It was not possible to get results for the first minutes since the measuring device relies on tension in both the middle strings. Secondly the stringing took twice the usual time (a lot of fiddling with measurement cables) so the the tension drop is probably a bit larger than usual (but with less drop afterwards).