The blade should lift slightly on the return stroke.
On my Q+S hacksaw if I drop the blade to just above the work, pause it using the hydraulic damper, then start the motor, the blade starts to lift (I quickly move the damper control to drop the blade on to the work).
The Q+S has a 2 positions for the damper control (plus fine adjustment).
There is a correct direction of rotation – on the Q+S this is marked on the crank drive wheel. You can check this as the connecting rod to the blade carrier should pull slightly down on the cutting stroke and push up more noticeably on the return stroke. If rotation is wrong it should be quite easy to spot.
Connecting rod should be close to parallel to blade on most of cutting stroke – noticeable angled to it for most of return stroke.