The actual text (from page 20 of TU&WA) is:
There is no chance for avoiding if the monster has surprised the adventurers and is within 20 feet, unless the monster itself has been surprised. If the adventurers choose to flee, the monster will continue to pursue in a straight line as long as there is not more than 90 feet between the two.Though initiative is not mentioned explicitly (in fact, as far as I know, initiative is not mentioned at all in the 3 LBBs), Hedgehobbit notes that "no chance for avoiding" does seem to imply that combat rules, whatever they are, become active if those requirements (surprise, within 20 feet) are satisfied. Now, in Satyavati's case, no surprise dice were rolled (though I suppose that a perfectly still statue suddenly moving could maaaaaaybe be considered surprising) so strictly speaking this rule would not be relevant.
Distance will open or close dependent upon the relative speeds of the two parties, men according to their encumbrance and monsters according to the speed given on the Monster Table in Volume II. In order to move faster characters may elect to discard items such as treasure, weapons, shields, etc. in order to lighten encumbrance.
The rule "distance will open or close" is difficult to manage without a grid or doing extra math. I actually prefer Hedgehobbit's version as originally stated. If a PC is within 20' of something, the combat rules are potentially in effect. If farther than 20' away, the pursuit rules are used (movement rates are compared directly).
This would have resulted in the outcome produced by the session, is easy to remember, allows players to reason about risk without introducing certainty, and seems intuitively reasonable.
The 20' threat range could also potentially be derived from monster movement rates (movement divided by 4, round down maybe) so that faster monsters would be more able to force combat. It might also be reasonable to factor reach into the equation, so that an ogre (with a movement of 9) would have a 30' threat range (9 / 4 = 2.25 + 10' for reach = 3.25, round down to 30' effective threat range). This also makes ranged attacks and missile weapons more dangerous, which is as it should be.