It is able to "interrupt" another spell and it allows for its effect to go first.
Not exactly. Divine Intervention resolves the same way any other Enchantment resolves and has to follow the same rules for doing so. Per the rules for an enchantment "You cannot interrupt an event to reveal an enchantment." You have to reveal it in between the various steps, phases, and actions of the game.
However, Divine Intervention can cause a spell or attack to fail and be canceled immediately via the ruling on Changing the Range or Target of a Spell or Attack, found on page 3 of the FAQ. In that regards you might consider it as an "interrupt" I suppose, since it can prevent events from occurring in their natural progression.
This could effect the casting of Mana Siphon, but it depends on who had Divine Intervention cast upon them. Mana Siphon targets a Zone. If the mage casting the Mana Siphon had Divine Intervention on them and it was revealed after Step 1: Cast Spell, then the Mana Siphon is cancelled and sent to the discard pile. This is because the Caster moved (even if it was to the same zone).
However, if the Divine Intervention was on the defending mage and you use it to teleport out of range, then the Mana Siphon completes it's cast and the caster now must choose a target of some kind for its effect (the only possible option being himself unless in a multiplayer game). This is because you do not resolve the effect of the spell, or choose the targets of the effect, until Step 3: Resolve Spell. The Divine Intervention does not actually interfere with the targeting of the Spell itself in this case.