It's quite simple in theory but can get a little tangled. In many cases it depends in what order you declare.
- However it's not possible to change the outcome to more than 20 on a d20 roll.
1, The target makes a d20 roll.
2,Target adds modifiers to the roll and sees if it succeeded or failed. (passive, from bless, inspiration, etc). Can use Portent or Lucky at this moment.
3, The Chronurgy wizard uses Convergent Future as a reaction to change the roll to "just succeeded" or "just failed, if possible within the 1-20 span.
4, The enemy can use his reaction (if he has any) to further modify the roll (if he is able to), possibly changing the outcome again. (Could use Lucky feat potentially)
Example with save:
Wizard's ally makes a Con save vs being petrified for example. The DC is 20. the Ally has +6 (+1 ability modifier, +5 Proficiency) to Con save and has Bless on him (+1d4 to save) . Rolls a 7 on d20 and 2 on d4 for 15 total and fails. Wizard uses his reaction to change the roll on the d20 to 12 and his ally succeeds. Wizard takes exhaustion.
Example with ability check:
Enemy is trying to escape the pc's, disengages, proceeds to jump across a chasm to get away. DM rolls D20 and adds modifiers (enemy has +7 to athletics let's say) and has a d10 inspiration on him. DC is 15. DM rolls a 3 and decides to use the inspiration for additional 5, bringing the total to 15, a success. The wizard changes the roll to 2 and the enemy plummets to his death at the bottom of the pit. Wizard takes exhaustion.
(Here it is a little tricky - the inspiration rule says you can add after the roll but before declaring success or failure. The Convergent rule says that you can change it after the roll (nor specifying whether or not after knowing the result). As those things aren't mutually exclusive, depends in what order you declare. If the enemy succeeded on the roll and didn't use the inspiration (rolled a 9 for 16 total and didn't use inspiration) and the wizard changed the roll to 7 (14 total), the enemy could still add his inspiration to succeed. Also if the DM in the example above rolled better on inspiration (7+), the wizard would not succeed as he can only change the d20 result and can't bring it below 1. Generally speaking as per RAW - the Convergent Future user can wait after the outcome is declared before using his ability.
Using this logic, Convergent future beats Lucky feat and halfling trait in some cases, also divination wizard's portent if the enemy uses them to make you fail and you override them (every time since Portent HAS to be made BEFORE the roll). However if you succeed and they cancel your success using their abilities, you can override them with Convergent. But again, things like Shield or Entropic Ward or Parry or sometimes inspiration (in the right circumstance) can thwart it again.)
Example with attack:
Enemy is a college of swords Bard Multiclassed with Bladesinger Wizard. Has a +1 studded leather armor, ring of protection +2, dex +3 and intelligence +5. On his turn attacks our Chronurgy wizard using defensive flourish and activating bladesong. Rolls an 8 on the d10 for the flourish, bringing his AC to 31 for the turn. Our wizard, out of spells and desperate, picks a fallen comrades Vorpal sword and swings at the enemy. He is not proficient with the sword and his Strength modifier is -2. With the sword's attack bonus he has +1 on his attack roll. He would need a roll of 30 to hit. If he doesn't roll it, he can bring his roll to 20 using the Convergent future. The enemy could react using his Shield spell, but that doesn't help against nat 20 and our wizard cuts the enemy's head off in one swoop, taking exhaustion.
If the enemy had a luck point he could potentially force a reroll of the 20. If our wizard had a luck point or Fortune's Favor on him, he could cancel the reroll. If our wizard rolled a 20 in the first place, the enemy could force a reroll using luck point and our wizard could then Convergent Future it back to 20.
So as you see it can get quite situational.
- But you can never "roll" less then 1 and more than 20 even using this ability.