Rulings
Q1: This card’s effect reads, “If WarGreymon or X Antibody is in this Digimon’s digivolution cards”. Does having a card with X Antibody in its traits count?
No. This effect specifies a card name, so you must have a card whose name is either WarGreymon or X Antibody in this Digimon’s digivolution cards. Having a card with X Antibody in its traits doesn't count.
Q2: I attack my opponent and perform a security check. Does this card’s All Turns effect cause me to gain 1 memory first, before the Security effect of the card I flipped over activates, or before the battle with my opponent's Security Digimon occurs?
Performing the check causes a card to be removed from your opponent’s security stack, causing this card’s All Turns effect to trigger. If you flip over a card with a Security effect, however, the Security effect will trigger afterwards, which means it will activate first. After that, if there are no other triggered effects, you'll gain 1 memory before the battle with the Security Digimon.
Data Sources
Lv.6 WarGreymon (X Antibody) BT9-016 SR Mega | Vaccine | Dragonkin/X Antibody Digivolve: 1 from [WarGreymon] [All Turns] When a card is removed from your opponent's security stack, gain 1 memory. [End of Attack] [Once Per Turn] If [WarGreymon] or [X Antibody] is in this Digimon's digivolution cards, delete 1 of your opponent's Digimon with DP less than or equal to this Digimon's DP.
Lv.6 WarGreymon (X Antibody) BT9-016 SR Mega | Vaccine | Dragonkin/X Antibody Digivolve: 1 from [WarGreymon] [All Turns] When a card is removed from your opponent's security stack, gain 1 memory. [End of Attack] [Once Per Turn] If [WarGreymon] or [X Antibody] is in this Digimon's digivolution cards, delete 1 of your opponent's Digimon with DP less than or equal to this Digimon's DP.
Lv.6 WarGreymon (X Antibody) BT9-016 SR mega | Vaccine | Dragonkin/X Antibody [Digivolve] [WarGreymon]: Cost 1 [All Turns] When a card is removed from your opponent's security stack, gain 1 memory. [End of Attack] [Once Per Turn] If [WarGreymon], [X Antibody] or [link = X Antibody (Card Name)] is in this Digimon's digivolution cards, delete 1 of your opponent's Digimon with DP less than or equal to this Digimon's DP.
Lv.6 ウォーグレイモンX抗体 BT9-016 SR 究極体 | ワクチン種 | 竜人型/X抗体 「ウォーグレイモン」から1【お互いのターン】相手のセキュリティが減ったとき、メモリー+1。【アタック終了時】［ターンに1回］このデジモンの進化元に、「ウォーグレイモン」か「X抗体」があるとき、このデジモンのDP以下の相手のデジモン1体を消滅させる。