Hi,
I recommended to use some glue remover to remove old glue from the backing board. New headlining will attach way more tightly, if you do this. I also glued small piece of foam to rear side of backing board. I used contact glue to do this. First glue foam part to backing card, then measure place where foam will be locate, when backing board is installed back. After that mark place to roof. Before installing backing board back, add some contact glue to marked place in the roof and to the other side of foam. Then wait about 20mins and press carefully headlining upwards with your hand. You will notice, when glue will attach. This will support rear side of headlining.
I have had this kind of fix in my car since 2013, without problems.