how does liquid pain work?

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This is also backed up, as newguy said, by monsters in the MM1, on more than one occasion, being cited as using SLAs of spells with long casting times in the middle of combat.

I still take it at face value that even using only the rules compendium as a single source, the description of "Usually, a spell-like ability works just like the spell of that name. A few spell-like abilities are unique; these are explained in the text where they’re described[...] Using a spell-like ability usually takes 1 standard action and provokes attacks of opportunity unless otherwise noted." Is pointing out that there are exceptions to the single standard action, much like monsters who can cast spells of longer cast time as a standard action in their own stat-block.

In this case, unless your method of gaining Liquid Pain as an SLA specifically calls out the change to the casting time or action, it would still take a full day. As gogogome pointed out, using Shadow Evocation trumps the 10 minute cast time of contingency, and like it, unless your method of gaining an SLA changes it, it become the exception to the rule "Usually takes a standard action", in this case, it is unusual.

With that said, if you are simply granting a player or creature the ability to cast liquid pain as an SLA, we're in homebrew territory, and then it does not matter what the rules say at all.