Translation:He spoke with me on the phone yesterday.
"Pelo" in this sentence has a sense of "through this mean". Ele falou comigo. Como? Pelo telefone. Através do telefone (through)
"Falar no telefone" it's more used when you are talking about the acting of speaking on the phone by itself. But if you say "ele falou comigo no telefone" it's correct as well, and people also say it like this.