Umm, that is crimp connector. Wire should be crimped, not simply pushed in. Photo is showing it inserted correctly, it just needs to be crimped using special pliers (of course you can use bit of solder and normal pliers). Add a bit of solder, then crimp with normal pliers and then heat it up again, so solder would re-flow.
Just be careful not to overdo it with solder as it might block connector.