Do you mean Manipulating the original footage's rectangles or Replicating the effect they have used to create it?

If your talking about Replicating the effect, here's how i'd go about it-
(preferably i'd use After Effects myself, but if you don't have it Prem Pro could do a version on it's own)

Take your footage lay it on the time line,
put atleast 4 more clips of the exact footage directly above each other so as they all run simotaneously.

Then lock the very bottom layer because this will never be touched!

now move along time line to where ever you want the first rectangle to start.
Turn the view off all of the clips except the clip above the original locked clip.

And use the Crop function to crop/slice the clip into the exact shape you are wanting

Now it's as simple as adjusting the Scale so as it's a little larger, once this is down, undo the eye icon of the clip below it so as you can now see the adjusted clip over the original footage,

Once this is done it's a matter of using the main tools Position, Scale, etc to move it to where you want it to be, shape it exactly how you think it looks good and getting the desired effect your after,
Being sure to use the Opacity function so as it's a little c-through and maybe even using a filter to give it a bit of a hazzy/blurred look etc.

then key frame it exactly where you want it to move, and bobs your uncle.

Now the reason i mentioned multiple layers of your footage is so that you can put a few rectangle etc on the screen at the same time all moving around.

Hope this helped.

it's really a matter of mucking around and tweaking it all to get precisely what your after!
Although to get much closer to what your watching on those titles, you need After Effects so as to change the enlarged, moving rectangles to a glassy, glossy, magnified look! but have fun anyway because with all the filters etc in Prem Pro you could get it pretty close!

In After Effects use a filter called- Track Magnify- it will do exactly what your after