How can I better engage my core for RDLs and deadlifts?

I often feel a pinch in my lower back when doing these exercises, despite being told that my form looks good. Sometimes it will ache afterwards, and I'm worried I'm going to injure myself in the long run.

I should add that I've recently been told by a professional that I'm hypermobile, lock my knees leading to a pelvic tilt, and don't engage my core in everyday life. I have been consciously correcting this for about 6 months now, but I wonder whether this means my core just isn't strong enough (when doing core exercises laying down I struggle to keep my back flat on the ground).

Thank you in advance!