When you activate (flip face-up) a Continuous Trap Card that has an Ignition-like effect, you can choose to activate that effect. The Ignition-like effect does not create an additional Chain Link. You simply state if you will also activate the effect of the Continuous Trap Card at the same time you activate the card itself.
Example 1: Player A activates “Stamping Destruction” and selects Player B’s face-down “Skull Lair.” Player B activates “Skull Lair” and says that she will also activate its effect, removing 4 monsters in her Graveyard from play to destroy Player A’s “Luster Dragon.”
“Skull Lair” resolves first and destroys “Luster Dragon,” then “Stamping Destruction” destroys “Skull Lair.”
Example 2: Player A has “Elemental Hero Neos” in Attack Position equipped with “Premature Burial.” Player B has “Malevolent Catastrophe” and “Ultimate Offering” Set in his Spell and Trap Card Zone. Player A attacks with “Elemental Hero Neos.” Player B activates “Malevolent Catastrophe” and chains “Ultimate Offering.” Player B says that he will also activate its effect, and pays 500 Life Points.
“Ultimate Offering” resolves and Player B Normal Summons a monster from his hand. Then “Malevolent Catastrophe” destroys all the Spell and Trap Cards on the field, including “Premature Burial” which also destroys “Elemental Hero Neos.”
Example 3: Player A activates “Monster Reborn” and selects a monster in Player B’s Graveyard. Player B can activate “Royal Oppression” and also activate its effect to negate “Monster Reborn.”