Hi! You've got the setup correct. There should only be one stack to draw from, and the five cards for each season row will likely be from different suits.
The season listed in each section's header applies to the aces and is there so players don't have to flip back to the setup page to check each time. For all other cards, you'll use the suit listed in the header and the value of your drawn card to locate the prompt. For example, the Hearts/Spring header means this is the section to find prompts for all heart cards, and the ace of hearts out to the left means you're in Spring.
Hope this helps!