
Not urgent. A drain field is a warm, wet, nutrient-rich zone a foot or two underground, which is the best habitat available to a root system. Roots do not break into sound pipe out of aggression — they follow moisture vapor to a joint or a hairline crack, push a fine root through, then thicken it. Once inside, the mass grows in the flow and blocks it. The failure being described is therefore a plumbing failure caused by a tree, which means it gets judged on the septic system's terms rather than on the tree's.
Years, quietly, and then all at once. Nothing here becomes dangerous in the tree sense — a tree over a drain field is not a falling hazard because of the drain field. What changes while you wait is money: the gap between removing a tree and repairing a field, versus removing a tree and replacing an entire system, and a failed field is among the more expensive repairs a house can present. If the property is going on the market, a failing field stops being a maintenance item and becomes a closing problem.