Yeah.... this is a can of worms.
I'll start with the works of the esteemed Thomas Jentz and work downhill from there. On page 190 of Jentz's; Germany's Tiger Tanks, D.W.to Tiger I, Appendix F, note 4, he states that "Zimmerit application began in August 1943" (on Tiger I's at least). Then on page 61 of Jentz's; Germany's Panther Tank, The Quest for Combat Supremacy, footnote 4.3.2, he states; "Starting in September 1943, Zimmerit was applied at the factory...".
Walter Spielberger's; Sturmgeschutz & it's Variants, page 100, states; "MIAG started applying Zimmerit protective coating towards the end of September 1943." However; "For unknown reasons, perhaps due to time constraints, ALKETT delayed the application of Zimmerit until the end of November/beginning of December of 1943." "ALKETT also deviated from the instructions by creating "waffle" patterns in the Zimmerit." So there is the origin of the Nov/Dec start time, but only for ALKETT. Spielberger cites the actual order as: "O.K.H. (Ch H Rüst u. BdE), 23.12.1943 76g Nr. 16975/43 In 6 (Z/Ing)." Go ahead, try googling that one...
Tom Cockle and Gary Edmundson's Osprey book; Modelling the Late Panzerkampfwagen IV, page 32 states; "Zimmerit was an anti-magnetic mine compound applied to the vertical surfaces of some German armored vehicles from September 1943 until September 1944."
I doubt that all the assembly plants were supplied with the materials, tools and training at the same time, this would lead to a staggered start time for application to begin. The end date is firmly established by OKH order on Sept. 9th, 1944.
I don't know what various websites use for references, since they don't usually bother listing them, but the authors I've quoted are some of the most respected in this field, especially Thomas Jentz.