And good luck to you. VTC5s, assuming authentic, are good batteries, for all they're not VTC4s. You are further correct to make 75 watts across a .08 ohm coil about 2.5 volts are required; 2.44949 to be exact. And three 3.7v batteries (nominal) do make 11.1v (nominal) in series. However, my point is the voltage is meaningless. Regulated mods use voltage converters of one or another type on the board; that's how they can vary watts without changing the coil resistance. A DNA200 uses both buck and buck-and-boost converters. Thus, the voltage required to drive a given wattage across your coil is meaningless because it is invisible to the batteries; it's on the other side of the board. The batteries give you whatever voltage they have at their then-current charge state, no matter what. It's the board that measures this, and changes the voltage to make your required watts.
And the point of all this is, it's amps that kill batteries, not volts. Note your .08 ohm, 75 watt circuit also draws 30.16862 amps (plus I^2R losses on the board, connectors, conductors, etc.), and this value is greater than 150% of the rated loading of three 20 amp batteries in series. While I do not know how it does it-- just a guess, pulsation-- I feel sure your mod somehow reduces the load to or below 20 amps to stay within the permitted draw levels of your batteries. Therefore, so long as you stick with regulated mods, buy good, authentic batteries, and your mod electronics do not fail on, you are unlikely to blow yourself up. That's why people use regulated mods, so they don't have to worry about boring old Ohm's Law. So I repeat: Good luck to you.