I am having this issue as well. I have yet to see the Deluxe content in my game and this is my Second playthrough. EA app says I have the deluxe installed but I have zero evidence of that in game.
Technically my "first" character crashed when leaving character creation: I failed to restart my computer between updating graphics drivers and hitting play. My bad- started over next day. So my first playthrough is actually the second character made. I got the notification about items, opened the chest and... nothing. None of the items showed up. Later on I got the N7 stuff but still no Deluxe things.
A month ago people were saying second characters were where the issues were and only first characters got the items; so I figured it was an oversight EA would rectify fairly quickly now that it had been noticed. I was wrong.
My current (and second) playthrough never even got the notification or chest and certainly not the items. But I got the N7 armor again and the Champions regalia came in just fine.
It is actually ridiculous that there is no solution to this yet. I pre-ordered the Deluxe edition. I paid for these Items! Yet over a month in there is still no solution to this? I have paid for something I did not get. This needs to be fixed.