Almost never. Healthy septic systems already have all the bacteria they need from household waste. Additives sold at hardware stores rarely help and can sometimes harm by disturbing established microbe colonies.
More detail
Septic tanks self-inoculate from human waste; the bacteria population establishes within weeks of system startup and self-regulates based on input load. Commercial bacterial additives (Rid-X, Roebic, etc.) sold at hardware stores rarely produce measurable improvement in healthy systems. EPA SepticSmart and Ohio Department of Health both note that no additive has been shown in controlled studies to extend system life or reduce pump frequency. Some additives contain solvents or surfactants that can actually harm the bacterial population by disrupting the established microbial ecology. The exceptions: aerobic systems sometimes benefit from a controlled bacterial inoculation after a major service event (aerator failure, prolonged power outage, or chemical introduction), but the inoculant should come from the system manufacturer or a service provider, not a hardware-store product. Cincinnati homeowner-spending watch: roughly $100-$200 per year on commercial bacterial additives is a common pattern for septic homeowners who think they are extending system life. The same money applied to a pre-paid pumping schedule (one $400 pump every 3 years amortized to $130/year) provides actual benefit. Hardware-store additives are a low-impact spend; pumping is a high-impact spend.