When setting a IMOD for a threshold and the TRIGLVL is set to PROBLEM, the IMOD is invoked when the status enters or leaves PROBLEM 

Is there any way to let Sysview execute the IMOD only when the status change to PROBLEM and do nothing when it change to NONE?

CA Sysview z/OS  any release

There is no way to avoid the IMOD execution when leaving PROBLEM status, but is possible to test the Status value, then simply exit when it is set not equal PROBLEM.
 For example, there is an IMOD called JOBCPU% in the IMOD library. It can be found the source in the CA Sysview library called  hlq.CNM4BISR in member GSVI0120. 

Here, there is a PARSE of the message received from the threshold and there is also the 'NewStatus' field.
Newstatus field  contains PROBLEM, when entering PROBLEM status, and NONE when exiting. 

So, to trigger something when it enters the state PROBLEM, then the IMOD should contain code like :
IF NewStatus = 'PROBLEM' then 
DO 
<commands> 
END 

Sysview documentation              : Threshold Exception Definitions 
CA Common Services for z/OS  :  REXX Language in CA GSS.