No email necessarily but they will see their own avios depleted at a pro-rata rate. Any avios booking you make, even just for you, takes avios from the pool and a portion will come from the partner's stash. Also, picking the other pax from your HHA will auto populate their details and it will appear in their app/MMB.

Best I managed was on a cash booking but didn't enter her BAEC number so it didn't appear in her account. Paid with BAPP which just showed the amount on the recent transactions, but when the statement was raised I discovered it was all itemised even including the destination - so it wasn't a surprise for long!