Remember your air vents

I've seen some sketches for rain barrel systems where the designer forgot to supply an air vent.

A bottom-filling sealed barrel won't hold much rainwater if air can't get out of the barrel.  Add a vent to the top, and remember to have the vent opening be higher than your diverter or collector barrel.

A sealed barrel system which fills near the top can also encounter problems if air can't also escape easily through that top pipe.  If you have a two-inch pipe from the diverter, and a two-inch opening into the barrel, you might be fine most of the time because usually there isn't more water than that.  As long as water can flow most of the time there will probably be more than needed to fill the barrels.

Remember to let the air escape so water can flow.  That is also the principle behind the drain-waste-vent (DWV) system that is probably in your house.  Any place where liquid is supposed to flow also needs an air vent behind and in front of it, so the liquid can flow downhill without fighting the air pressure and so the liquid won't create air pressure which will cause problems.