Does the Vivilion postcard pinning overflow to the next medal

Your player level impacts the maximum CP level of all Pokemon, not just the ones you catch after levelling.

You can clearly see this mechanic by comparing the CP circle behind the Pokemon. After you level up, the "filled in" area will decrease, to reflect the increased maximum.

You may notice higher CP Pokemon also spawn, as your higher trainer level also allows you to catch higher CP Pokemon.

It's a bug in the game due to server or connection problems.

Note however that you will usually be refunded health and special move charge back to when you should have killed the opposing Pokemon. In your case if you check your Pokemon it's likely (although not guaranteed) that the two other Pokemon will still actually be at full health.