Does adding turmeric to meat marinade negate the bacterial buildup at room temperature?
From the description in your question it looks like you're from India and Indian cuisine uses its native spices optimally and turmeric is proven to be antibacterial, however:


  How it works is still something of a mystery. The researchers know that curcumin tends to hang out within the bilayer more than in the vesicle’s central space. They suspect that when the sugar on the vesicle surface sticks to the cell wall of a passing bacterium, curcumin migrates into the cell and kills it from the inside.


Now onto the question what you should do: will the marinade be as tasty if you put it in the fridge?  Yes, of course, so both granny and you are correct:


Turmeric is antibacterial (though not a total disinfectant)
Putting the marinade straight into the fridge and leave it to marinade for 2 hours at 5°C will work nearly as well as leaving it out in 20-30°C from a pure taste perspective.


So use the best of both worlds: use granny's herb mix and refrigerate!

P.S. I leave my marinades for 2-24 hours in my fridge and I'm from a much cooler climate than you...
P.P.S. Don't freeze as -21°C will slow down the marination process too much and −273.15°C (absolute zero) will stop it completely!  ;-)