What adjustments can you do to prevent psoas tightness in an aggresive postion on a road or track bike?
When they say activate the core, they mean you should also actively use the muscles on the front of your belly and inside. Not just your back. It definitely does not mean you should be overstressing your rectus femoris or psoas.

Something has to hold your posture. Hands do some of the work, but also cannot take too much, because then they become tired and numb. So than the spine and the muscles around it take a lot of stress. Mobilizing the core means taking some of this load from the back muscles.

I recommend this one where the topic is discussed on an actual bike saddle in the other half of the video.


                
            

One has to use the abdominals to held the position, not just leave everything on the back muscles. The context of the video is the pressure on the saddle. But when you watch the pelvis and the lower back when he loosens the abdominals, you can also imagine the stress on the psoas.



There are many articles and videos about core exercise specifically directed to (road) cyclists. For example:


                
            


                
            

Getting those muscles stronger will enable using them for holding the posture and relieve some other parts. If you only look for stretches, it may not be enough for you.