If your plants have been in those pots for four weeks, their root system should be well-developed, meaning your AutoPot system would be ready to be hooked up. I typically connect mine about 10 days after transplanting to AutoPots.
However, I may have some bad news—your plant is likely stunted, and I expect it will continue to struggle throughout the grow. The issue is that you’re using coco without perlite or another aerating amendment. If I remember correctly, AutoPot recommends a 60/40 coco-to-perlite ratio when using their system. The reason is that coco holds moisture extremely well—so well, in fact, that with the AutoPot system constantly providing water, the roots can become deprived of oxygen.
I see you’re using the AirDome system, which helps, but without perlite, it won’t effectively aerate the substrate until the roots have reached the very bottom of the pot. Until that happens, they’re likely not getting enough oxygen.
To try and save the grow, you’ll need to encourage root expansion. This may sound counterintuitive, but I recommend stopping watering until the medium dries out significantly. This will force the roots to grow outward in search of moisture. You may need to repeat this process a couple of times before hooking up the reservoir. Right now, the roots likely have no incentive to expand because the coco is keeping them constantly moist. Drying it out periodically should help promote stronger root development and give them a better chance at reaching the AirDome