The Spirit procs from Vindicta's Flight and Wraith's Full Auto are being applied to enemies who attack them while their Return Fire is active, making Return Fire significantly more lethal when it is held by either of these two characters.
Playing as Bebop, if you stealth with Shadow Weave, fully pre-charge your laser by aiming down sights (default RMB), and then fire afterwards, you will leave stealth without getting the Ambush buff from Shadow Weave.
As mentioned earlier, this is not something specific to Monster Rounds. Any equivalent source of Weapon Damage (35% + 6% in this case) would give you the same results. And the impact will vary wildly by character. You can test with Abrams to see an extreme example on the opposite end of the...