Mulch mentions a note being sent back in time when he realises the two are time travelers.
The dwarf was actually doing a little jig now. "No. No, it all adds up. You're talking about future events in the past tense. You sent back a note so that I would come and rescue you here and now"
Artemis Fowl: The Time Paradox, Ch 6, p 109
When they come back to their main timeline, they ask Number One if they could send a note back in time so that Mulch could save them.
"I need you to send a note back in time"
"I've been ordered not to open the time stream again, but maybe we can squeeze back one more thing," said Number One.
Artemis nodded. "That's what I thought."
"When and where?"
"Holly knows, you can do it from Tara."
"How do you spell stupendous?" said Holly, smiling.
Artemis Fowl: The Time Paradox, Ch 16, p 359