Here is what you should take away from this link:
"Fast effects are card activations and effects with a Spell Speed of 2
or higher, including monster Quick Effects, Quick-Play Spell Cards, and
Trap Cards (which includes both activating Trap Cards, and activating
the effects of things like Continuous Trap Cards)."
Go down to the chart at the bottom. We start at section A and will go down the path to the left.
1. The game state is open. (occurs at the beginning of every phase)
2. Turn player takes an action that does not start a chain. (i.e., normal summons Rescue Rabbit)
3. Does this activate a triggered effect (i.e. Stumbling, Level Limit Area B ... etc)? We'll assume a clear field so answer is no.
4. Turn player can activate a fast effect (looking back up at the list of fast effects, we see that monster ignition effects are not listed, therefore you cannot activate Rescue Rabbit yet). We'll say turn player activates no fast effects.
5. Opponent can activate a fast effect. (i.e. Effect Veiler or Chain Disappearance)
Since Rescue Rabbit's effect is not spell speed 2, it cannot chain to Effect Veiler or Chain Disappearance, so both can now be used against it successfully.