any kind of pressure against the quill just unscrews the handwheel instead of boring a hole in to a blank.
Actually, I think that's basically normal - turning the handwheel in the clockwise direction (viewed from the right end of the lathe), advances the screw to extend the ram to the left (toward the headstock), so if you push the ram in the opposite direction, it will want to spin the handwheel in the counterclockwise direction. And if the ram and screw are lubricated, and if you aren't holding the handwheel, it can just spin on its own.
As Ken B said, tailstocks are really simple mechanisms. Here's a cross-sectional sketch of how the components of a typical headstock fit together. The leadscrew is pinned to the handwheel by means of a small grub screw (which typically has a hex socket head). The leadscrew is held in place because the larger diameter is larger than the hole in the tailstock casting, and the handwheel prevents it from moving to the left. Therefore, the leadscrew can rotate but cannot move laterally. At the same time, the ram is attached to the leadscrew by means of the coarse threads which means that it moves laterally; if the ram moves too far to the left, the threads uncouple and it has to be manually pushed back onto the screw, and it can only move to the right until it encounters the tailstock casting at which point it stops. (There is another grub screw that is not shown in this sketch. It is threaded into the side of the tailstock casting and rides in a groove machined into the side of the ram; when that screw is loose, it prevents the ram from rotating. When it is tight, it locks the ram and prevents lateral movement.)
When I'm drilling, I use my right hand to turn the handwheel in a clockwise direction to advance the bit into the wood, and I have my left hand (in a protective glove) on the chuck body to prevent it from spinning freely when I withdraw the bit. I know it's possible to advance the bit by sliding the entire tailstock assembly to the left, but I find that using the handwheel provides better control.
Are you trying to drill by sliding the entire tailstock to the left to advance the bit into the spinning blank? Putting pressure on the ram while not holding the handwheel will cause the handwheel to spin. You can advance the drill bit by sliding the entire tailstock assembly to the left, but if the ram is extended, that will cause the handwheel to spin and the ram to retract back onto the leadscrew, but only until it reaches the end of the threads..