I think I know what it is. The notifications (currently) get sent only to the specific user/access ID who set up the payment, so if you and your partner are sharing an access ID then you may not receive an alert if your access ID didn't set up the transfer.
So, that probably sounds a bit complicated, but in any case, if you are sharing one access ID between you and your partner, then the owner of the actual access ID you are logging in with would (or should) have received the notification if the owner of that access ID had set up the alert rule and had the right contact details loaded.
We debated this situation heavily when we built this alert with this in mind. In a perfect world we believe each customer should be using login details that are unique to each user, so this is something you could do then both you and your partner can receive whatever notifications or alerts you prefer.
But either way, apologies if any of this has been frustrating for you, if it is the situation above, then our recommendation is that each party of a joint relationship has their own login details then you can make sure you set up the alerts that suit you.
Does that help or make sense ?