The RAW state that a blunderbuss has the follow property:

Explosive. Upon a hit, everything within 5 ft of the target must make a Dexterity saving throw (DC equal to 8 + your proficiency bonus + your Dexterity modifier) or suffer 1d8 fire damage. If the weapon misses, the ammunition fails to detonate, or bounces away harmlessly before doing so.

Does this explosive property target the character/NPC firing the weapon if the firer is 5ft from the target? My assumption is no. The effect of the shot should be oriented away from the gun.  I also assume the forward blast should be in a cone shape but the description does not specific.

You are within 5ft of the explosion, so yes. 

This really does not pass a firearms physics test on how this weapon functions in RL.  Looks like a HomeBrew rule is needed at my table.

The blunderbuss does not have the explosive property, only the [Tooltip Not Found] (literally a grenade launcher) does. The explosive property is defined in the description because the same information is used in every CR firearm. The weapon actually lists what properties it has under "properties."

Actually, the item's page doesn't have the complete information about its reload and misfire property values. So check the firearm chart in the gunslinger subclass.

Thank you. This is makes more sense.

Quote from Alpinist >>

This really does not pass a firearms physics test on how this weapon functions in RL.  Looks like a HomeBrew rule is needed at my table.

 None of the rules for firearms in D&D really pass the smell test for how firearms work in RL.