I believe doDateDelta and doDateDeltaFromCurrent use Simple Date Time formats. I do not know if there is a format that produces epoc time.
In a JSR or Scripted Assertion before the Responder Step (or prior to any custom logic that might be performing a parseInState on the VSI response object), generate the epoc:
long epocTime = System.currentTimeMillis() / 1000L;
testExec.setStateValue("UNIX_epoch_time", Long.toString( epocTime ) );
I don't care for spaces in property names, so in your VSI response example, I would do this:
"issued_at": {{UNIX_epoch_time}},