Not sure if about the pressure pump with a built in bladder. I recently purchased and plumbed a jet pressure pump 20 psi ON to 50 psi OFF, that pumps into a pressure tank with a bladder to sustain pressure. This bladder tank holds 50 gallons of water. The storage is from a 3,000 gallon concrete holding/storage reservoir that the Well pumps into. A nice setup to prevent too much on and off cycling of the Well pump.
If a sand or gravel pack filter is plumbed into a roof catchment system it should be plumbed for backwash cycles or it will eventually plug off or need to be repacked it would be advisable to occasionally treat with NSF Chlorox bleach target dosage 6/7 drops per gallon to achieve 1 part per million safe levels for human consumption but wil slow slime growth and disinfect the filter. It should also be mentioned to route the roof water into a standpipe with a small hole drilled into the bottom of the pipe to waste the first flush indroduced as the first rain fall water is collected this will waste the dust/dirt/bird droppings etc...then as the pipe fills to a larger diameter hole that water is routed to the storage barrels.
Keep in mind all the water on this Earth has passed through a living creature at some point in time!