If you shift in manual mode, you are asking the transmission to work more like a manual transmission than an automatic. In other words, when you pick 1st, 2nd, 3rd, etc., you are eliminating the torque converter’s spinup of the impeller blades. In turn, these blades begin to move the transmission fluid through the entire transmission.
Normally, the transmission fluid whooshes its way through the gears as the changing gear/clutch/band sets engage and disengage in response to valve body inputs as well as solenoid actions. However, when you are in manual gear, you essentially lock up each gear until you hit the next one. In this manner, there is no slippage — except for minor mechanical and built-in fluidic losses that will occur anyway. Instead, there is a hard connection. The proper settings are forced and the transmission works correctly.
What I think is happening in your transmission — you have pretty much confirmed it with your detailed description — is that your Mazda is down a bit on transmission fluid. What happens is that the level is just high enough to keep things working but not without problems. In this case, the transmission has to work harder to provide enough pressure to make sure that the transmission parts work correctly. And, since there are times when there just may not be enough fluid available, as in a turn when you are accelerating, then the gears/clutches/bands that were engaged correctly, lose their connection because the fluid level drops too far.
Check the tranny fluid level first. I think you’ll find the transmission is down about a quart.
