My understanding is that NI-VISA doesn't support internal monitor function in itself.
If you are using Tektronix USB connectable indtruments such as DPO4000 etc. then Tektronix VISA
named TekVISA is a substitution and it supports CALL MONITOR feature logging all input and putput
stream with saving capability and getting timestamp data.
I think both Tektronix VISA and NI-VISA are developed based on VXI standard specifications and have
a compatibility from the viewpoint of fundamental functions such as viOepn, viClose, viRead and viWrite
and so forth.
Hope this helpful to your work.
If your issue is not relevant to my understanding then I apologize.
Best regards,
obaq