No. You should never transcribe all dialogue as quotations within interview transcripts.

For transcripts containing voice overs, you would transcribe the dialogue as normal. For the voice over, you can use a convention — i.e., [VOICE OVER] — or put it in italics.

For example:

Introducing Chaunte, the Wayans family’s most talented member.

HOST: Great to have you here, Chaunte.

MS. WAYANS: Thank you for having me.

Or:

[VOICE OVER] Introducing Chaunte, the Wayans family’s most talented member.

HOST: Great to have you here, Chaunte.

MS. WAYANS: Thank you for having me.