Betadine disinfects with iodine. Iodine is not a particularly good disinfectant for a hot tub. In fact, it can actually reduce the effectiveness of either bromine or chlorine as a disinfectant because any chlorine or bromine would get used up oxidizing iodide to iodine.
Betadine needs to be used full strength to disinfect. If it was used to wipe down the empty tub, that might disinfect the surfaces, but it wouldn't get in the plumbing. If it was added to the tub when full of water, then it would be too dilute to work well especially on any biofilms.
Bacterial infections from hot tubs happen when insufficient sanitizer is maintained. This can happen if the level of chlorine or bromine is too low for any appreciable amount of time.
It can also happen if too much of the chlorine gets locked up by high levels of cyanuric acid. This can happen from excessive use of dichlor.
A similar thing can happen if too much of the bromine gets locked up by dmh from excessive tab use.
If bacteria is allowed too much time, it can form biofilms in the plumbing and equipment.
Biofilms provide a reservoir of bacteria that can continue to reinfect the bulk water any time the sanitizer drops below a safe amount.
I would suggest a full decontamination including a purge product to clean out any biofilm.
http://www.troublefreepool.com/threads/9670-How-do-I-use-Chlorine-in-my-Spa-(or-pool)
Ahh-Some
See this chart