You have a conflict.
You're telling the system you want the spa AND the pool on from 3-9PM.
Your pool schedule needs to begin at 9AM and end at 3PM, to provide an opening for the spa schedule.
I also habitually offset them by 1 minute to eliminate panel hiccups. In other words, your pool schedule ends at 3PM and the spa schedule starts at 3:01PM. Not absolutely necessary, but you'll know it will do what you tell it to do.
For clarification, you also said, "I know the spa pump does work" and this needs to be addressed. The filtration pump runs both bodies of water. It's only one pump. Hayward lists this in a way that confuses a lot of users because Pool and Spa each have a menu and it makes you turn "on" the filter pump in that respective menu, leading to the assumption you have two pumps. For example, if the pool schedule is running, all that manually enabling the pump in the spa menu will do, is change the valve positions.
Unless, you are reffering to a jet pump, or you don't have a spa built into your pool/spillover, in which case we will have a very different discussion.
P.S. if you have an Omni, I'm assuming you have a VSP. You should run the pump 24/7 if so. Pick a speed between 1500-1800rpm (medium).