iPhone does not vibrate while recording

The answer is that Apple doesn't allow this. All audio sessions that allow recording turn off vibration.

Do you need to vibrate and record at the same time?

If you don't, you can stop your audio unit when it's time to vibrate, change the audio session type to live audio, play the vibrate system sound thru audio services, then switch the session back to play and record, and restart your audio unit recording again.