Door sensor - thinks door is open if the door is pushed in

We've had Xfinity home security for eight years, but last week it was replaced with the wireless sensors because our old wired system burnt out. The other night, our alarm went off in the middle of the night because it thought that our front door had been opened, even though it hadn't been and was securely locked. In the morning, we tested it out. It seems that if the door is closed, it does register as "closed"... but if we push the door further in (to make sure it's firmly closed) the sensor says that it's now open. I can barely tell that there is even a difference, but the sensor can.

As far as we can tell, the door moved slightly at night because it was windy. We'd rather not have this happen again. Is there anything we can do with the sensors to prevent this?