Well not only the strap tightening thing could be the issue, so try that and see if it cures the issue, if not then it may be you got the wrong size shoe, too small will jam your toes (especially the larger ones) into the front of the shoe and pinch the nerve which in time numbs the toes; too large can make your feet move to much and slide forward in the shoe and again pinching the nerve.
Cleat positioning could be off, make sure the cleats are in a position that allows middle of the pedal to be in alignment with the ball of your foot, you can figure this out easy enough by being in the shoe and feel for that bony protrusion of the metatarsals and place a tape where you feel it, next put the shoe into the pedal and see if the tape is in alignment with the pedal spindle. If that placement doesn't work and your toes still get numb then try moving your cleats towards the heel of the shoe and see if that works.
There are other things you can do to like getting a pro fit, getting orthotics, changing pedals etc, but since you didn't have this issue before I doubt seriously anything physically has changed so those more expensive things to do is probably unnecessary.