The Blowgunner has a large aggro radius but unlike most ranged enemies, they will not attack through walls or solid platforms. At 4+ BSC, they will not teleport to chase the player.
If the Blowgunner is too close to the player or they are not in attack range, it will leap to a different platform. It cannot shoot the player from below.
Blowgunners are dangerous ranged enemies. They are more agile and fire faster than other ranged enemies like Inquisitors and Bombardiers, can run away from the player pretty quickly, and spawn in higher densities and can easily be found in groups. However, to compensate their projectiles do not go through walls or platforms and they cannot fire above them.
The way to approach them is to avoid open spaces and try to approach them from directly below. If one can get close to them without causing them to attack, they will try to jump away, giving one time to hit them. Approaching them from above is easier because they won't be able to attack, but if going up is necessary, try to get to higher ground as quickly as possible and try to kill them before they can jump away.