Consider the effects of ozone to be secondary to chlorine. Ozone is an excellent backup to chlorine, but you absolutely still need a chlorine source for residual sanitizing power. Ozone does not provide any sort of residual - think of it like a super-instant-clean with zero lasting power, that only cleans the bits of water that touches the ozone gas. Not all of the water will touch the gas unless you run the ozonator long enough, but you also don't need it to either, so long as you have a free chlorine residual.
If you can, time your ozone to run immediately after your soaks for 0.5-4 hours (test the timing to see how quickly the ozone burns through your chlorine - see below about that). The post-soak ozonation will clean up waste quickly, and then add enough liquid pool chlorine to get to 6-10ppm FC in order to maintain a sanitizing residual in the water, keeping your water clean until your next soak. Ozonators usually run with filtration cycles and heating cycles, and only if the spa control panels have not been touched, as some manufacturers don't want to output ozone while spa is actively in use - check your owner's manual or techbook to confirm.
If your ozonator will continue to run after you add the liquid pool chlorine, shoot for 10ppm FC. The reason is because ozone destroys the hypochlorite ion to produce 77% chloride and 23% chlorate per the following reaction:
Chloride reaction: O3 + OCl- --> [ O2 + Cl-O-O- ] --> 2O2 + Cl- (77%)
Chlorate reaction: 2O3 + OCl- --> 2O2 + ClO3- (23%)
Basically, you will see much higher (~50% or more) chlorine demand (aka consumption, burn, utilization, destruction) whenever your ozonator runs. You want enough free chlorine to be circulating and sanitizing before the ozone destroys the chlorine, so you need to find a balance between ozonation and not destroying your free chlorine too quickly before it gets a chance to thoroughly sanitize the spa. If your ozonator is powerful and effective (e.g. Bullfrog EOS system), at 4 hours of daily ozonation (4hr filtration cycle), it can take your free chlorine below 1ppm within 3 days. This isn't necessarily a bad thing - if your spa is well sealed, the plumbing is biofilm-free, and the water and all surfaces are already sanitized from the previous free chlorine killing everything in sight, and no bacteria is growing on the underside of your cover, then having a sustained low FC level shouldn't be a concern since there is no bacteria in the closed-system to cultivate.
However, prior to your next soak, you should raise FC to 3-6ppm, since going in for a soak will shed billions of bacteria off your skin and into the water instantly, some of which can multiply very quickly (some populations double every 20 minutes) when there is <3ppm FC.
Free Available Chlorine Germ-Killing Timetable
E. coli 0157:H7 (Bacterium): less than 1 minute
Hepatitis A (Virus): approximately 16 minutes
Giardia (Parasite): approximately 45 minutes
Cryptosporidium (Parasite): approximately 15,300 minutes (10.6 days)
Note: Times based on 1 ppm free chlorine at pH 7.5 and 77°F (25°C). These disinfection times are only for pools and hot tubs/spas that do not use cyanuric acid. Disinfection times are longer in the presence of cyanuric acid.
Source:
Disinfection & Testing | Healthy Swimming | Healthy Water | CDC
I find the following article about ozone to be excellent and unbiased:
Unfiltered Truth About Ozone in Hot Tubs - many (most) other websites have some incorrect information mixed in or are heavily biased towards selling ozone generators without noting the many caveats required to substantiate their claims about the benefits of ozone.