The best amateur research I've done indicates the cordisol provided to your body by the Prednisone is most effective when taken first thing in the morning, and is less effective as the day progresses. This is due to the body's normally natural Cordisol release being based on your body's circadian rhythm. There's something called a circadian Cordisol "slope" .... High in the morning and diminishing toward evening. This why you should also get out into the sun in the morning, and avoid waking up in bed for extended time in a dark room. But it's also why you why you want your highest physical activity to occur in the first part of the day, and slow down towards evening, .... avoiding staring at a bright screen in bed at night.
This information I have personally found useful and experienced results

Hubberman...
Circadian Rhythm affect on the daily Cortisol curve, stimulated by morning light

Start here: 2:25 but the "kicked" starts here: 3:45

Same topic but very long lecture

Start here: 17:00 but "kicker; is here; 21:00

Dr C
Mythology of Adrenal Fatigue

Herbs to stimulate Adrenal Function