I think either would do in normal speech. And I think there are plenty of other contexts in which you might be likely to encounter such usages of the present perfect for the very recent past.
Conversational English is quite forgiving of people using present perfect forms for things that were the case until the very recent past. Especially when two parts of a sentence are separated by a conjunction ('and' or 'but' in particular).
"I've been getting bored here in the café alone, but then you came along."
"James has eaten the whole piglet, and threw out the bones a few minutes ago."
If we really wanted to be Mr Logic about it (and when talking about grammar, we often do!) we might point out that a switch of perspective happens mid-sentence, but in my opinion, that switch is fine and dandy.
After all, the conjunctions 'and' and 'but' are generally used to join two otherwise complete and independent sentences.