Why reverse connected MOSFET start to turn on at Vgs<Vth?
Why does the reverse connected MOSFET starts to turn on from about Vgs >= 0.4 V when the published Vgs(th) value is 0.65V minimum?



Statements below regarding polarity are made for an N Channel device.
The equivalent P Channel statements also apply.


The results that you are seeing are due to (well known to industry but less known in popular understanding) assymmetric behaviour of MOSFET Vgs / Ids characteristics at Vgs values both around and below Vgs(th)_forward.   

Specifically, Vgs(th) may be effectively lower o even vey much lower when Vds is negative (but necessarily &lt;= Vf(body_diode) and Ids_max may be very substantially higher for a given Vgs when Vds is negative. This is exactly the results that you are seeing.


Examination of Fig A.1 below and the related text provides an essentially complete description show WHAT you are seeing happen.  
For a description of WHY (for the brave :-) ) see the cited reference and related material below.


Note that while the paper indicates that the information relates to TRENCH MOS devices it also notes

    This characteristic behavior is not exclusive of trench MOS technologies 
    as it may also occur in other types of vertical MOSFETs such as DMOS, 
    CoolMOSTM, and planar structures.


Their following summation explains what you are seeing.
Note that the numerical values relate to the device they are dealing with and are similar in nature but somewhat different in absolute values to your example.  

"From the measurement results it can be observed that:  


The body diode forward characteristic seems to be modulated by voltage Vgs in
the sub-threshold region, even at negative Vgs values down to 1 V [for the device in question].  
At a given Vgs in the threshold region (i.e., voltage Vgs close to Vgs(th)), the
drain current magnitude in the third quadrant is much larger than that in the first
quadrant, also at low  Vds. For instance, at Vgs = 2 V and Vds = -0.5 V the drain
current reaches 40 A. In the first quadrant however, the maximum drain
current at the same Vgs is about only a few amps.
A symmetric characteristic between the first and third quadrant appears ... 
at high Vgs.


_____________________________________________

This 15 page appendix Third Quadrant DC Output Characteristics of Low Voltage Trench MOSFETs* provides a useful introduction to the subject, and there is much other material available 'on web'. 


*In text   T. Lo´pez et al., Voltage Regulators for Next Generation Microprocessors,
DOI 10.1007/978-1-4419-7560-7, # Springer ScienceþBusiness Media, LLC 2011


The following quotes (edited for brevity) are drawn from the above text:


In the following subsections the third quadrant output characteristics is described
in more detail by looking at the internal structure of the device and analyzing the
origin of this significant reverse current conduction.
Semiconductor manufacturers typically specify the DC output characteristics of
power MOSFETs in datasheets, ... Yet, such specification only refers to the operation in the first quadrant, ... . Regarding the third quadrant, i.e., voltage
Vds is negative, only the body diode forward characteristic is usually specified for
zero volts Vgs. No further information about the channel current in the third
quadrant and its Vgs dependence is provided.

In circuit simulations ... 


it is usually assumed that the first and third quadrants are symmetric   
and that the body diode forward characteristic is independent on vGS [1, 2].
.


As shown in Fig. A.1, such assumption is not always valid. The plot depicts experimental results
corresponding to the output characteristics of an N-channel power trench MOSFET
(PHB96NQ03L)




______________________________

Your device behaviour for comparison.
If the device behaved symmetrically you would expect the 'yellowish' body diode limited curve to extend out until about Vgs(th)_forward at about Vgs = 0.6V 





Related:

This reference Power MOSFET Basics by Alpha-Omega Semiconductor -  who provided the coted datasheet and presumably the correct LTSpice model, covers the observed behaviour in its graphs but seems to miss the points raised above (see page 4) in its text !

The above cited paper is cited in a number of web documents  

The cited appendix is taken from this book - Voltage Regulators for Next Generation
Microprocessors - copyright Springer, 2011.