The closest I can find is on page 65 of the DMG under Spellcasting in Melee.
Attacks directed at spell casters will come on that segment of the round shown on the opponent’s or on their own side’s initiative die, whichever is applicable. (If the spell caster’s side won the initiative with a roll of 5, the attack must come then, not on the opponent’s losing roll of 4 or less.) Thus, all such attacks will occur on the 1st-6th segments of the round.
So I guess attacks are supposed to happen on segments 1-6 (inverse of the d6 roll?) and that is when spells begin casting?
Ah but then you have weapon speed factors on DMG page 66-67
Other Weapon Factor Determinants: The speed factor of a weapon also determines when the weapon strikes during the course of the round with respect to opponents who are engaged in activity other than striking blows. Thus, suppose side A, which has achieved initiative (action) for the round, has a magic-user engaged in casting a spell. Compare the speed factor of the weapon with the number of segments which the spell will require to cast to determine if the spell or the weapon will be cast/strike first, subtracting the losing die roll on the initiative die roll from the weapon factor and treating negative results as positive. Example: A sword with a factor of 5 (broad or long) is being used by an opponent of a magic-user attempting to cast a fireball spell (3 segment casting time). If the sword-wielding attacker was represented by a losing initiative die roll of 1, the spell will be cast prior to the sword’s blow. A 2 will indicate that the spell and the blow are completed simultaneously. A 3-5 will indicate that the blow has a chance of striking (if a successful “to hit” roll is made) before the spell is cast, arriving either as the spell is begun or during the first segment of its casting. Suppose instead that a dagger were being employed. It has a speed factor of only 2, so it will strike prior to spell completion if the initiative roll which lost was 1-4 (the adjusted segment indicator being 1, 0, 1, 2 respectively) and simultaneously if the die score was a 5. If the weapon being employed was a two-handed sword (or any other weapon with a speed factor of 10, or 9 for that matter) there would be no chance for the reacting side to strike the spell caster prior to completion of the fireball. Note that even though a spell takes but 1segment to complete, this is 6 seconds, and during that period a reacting attacker might be able to attack the magic-user or other spell caster prior to actual completion of the spell! If combat is simultaneous, there is no modification of the weapon speed factor.
So weapon speed counts as segments similar to spell casting time segments, but only if not engaging someone who is also trying to trade blows with you (unless you tie your initiative roll that round in which case it is pulled back in for who goes first in striking, unless closing in which case it is weapon length that goes first).