Linguist, thank you for answering. But I couldn't get for what I was looking from your reply. When you say this phrase, you say it like:
When we say the phrase, yes, it is said like the first way you said. Most British English speakers will pronounce 'potato' like the first way there - with the diphthong. However, for the purposes of the song, and phrase, you need to say the potato using both pronunciations.