Connect the Time to current time and the action to the on port as shown

You may wish to save this little setup for future use, basically we now have a frame controllable emitter, why Pstorm does not come with a built in stop start I do not know !!

While we are talking about frames change your project settings to 250 frames

OK lets get this cube to the party, in xpresso right click and add a Pshape node

To get the cube to be recognized as a particle go into plugins and then TP and particle geometry

make the cube a child of the particle geometry object

Connect the particle birth port on the Pstorm to the Pshape

Now add a bulge deformer

Make it a cild of the particle geometry NOT the cube as you would normally do. you see we want the particles deformed and not the original cube

The bugle deformer should be placed at world center around your sphere by default, if not position it around your sphere

Here are the settings for the deformer, ignore the coordinates, just make sure yours is around the sphere