If you’re concentrating on a spell and you cast another concentration spell, does the first spell end *immediately* upon casting?

Speaking of concentration,

If you're concentrating on a spell (i.e. Delayed Blast Fireball) & you cast another conc. spell, does the first spell end *immediately* upon casting, or does end once the second spell's effects activate – lingering until you begin concentrating?

— Slayer Kast (@SlayerKast) January 10, 2019