It's largely a matter of personal choice or habit while the video below will show you the WHY of good caulking technique.
Pushing forward forces the compound into small cracks and helps it to stick on smooth surfaces.
Pulling is easier for filling large cracks, and leaves a bulge which allows nicely for shrinkage without pulling away from either side. Avoid pulling it while laying the bead down so gently as to not have it stick to the surface or penetrate cracks.
The video shows important details on how to tool caulking and using a backer and release agent in large fillings.
Click here for information on which caulking to use.