The image is outside of my house where the down drain leads away from the house. The water flows in the direction of the arrows, and leak occurs where the "T" connector connects to the outlet. I tried pushing the T-connector into the outlet more, but it didn't help.
Best Answer
This type of pipe and fitting is meant for burial and is not made to seal. The pop-together fittings just ensure the pipe stays together, not leak free.
If you want water tight sealing on the joints, you need to use PVC thinwall sewer/gutter drain pipe. It will have the same adapters so you can get a proper water-tight seal for the sump pump drain, a nice rectangular adapter for the downspout and glue-together slip fittings that can be cement welded for permanent leak-free operation.
Barring that, you could try popping the connection back apart, get some poly-foam backer rod, tack it into the corrugation that will be inside the connector with some silicone and see if you can make a water seal with that. It will only have to cover 2/3 of the circumference on the bottom side of the joint.