Dispel magic ends the effect on only one target
1. This is a confusing area. RAW would appear to suggest that dispel magic should end the effect on both targets:
The rules for twinned spells state:
When you cast a spell that targets only one creature and doesn’t have a range of self, you can spend a number of sorcery points equal to the spell’s level to target a second creature in range with the same spell (1 sorcery point if the spell is a cantrip).
They are targeting a second creature 'with the same spell'. The caster does not cast the spell twice - it is still only one spell.
Bearing that in mind, the rules text for dispel magic states:
Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends. For each spell of 4th level or higher on the target, make an ability check using your spellcasting ability. The DC equals 10 + the spell's level. On a successful check, the spell ends.
So, if the caster of dispel magic targets either of the characters effected by the spell (in this instance haste), then the spell will end. It won't just end the effect of the spell on that character - the whole spell itself will end.
2. However, Sage Advice has rendered the above argument incorrect:
On page 14 of the linked Sage Advice Compendium it says:
Q: If dispel magic targets the magical effect from bless cast by a cleric, does it remove the effect on all the targets?
A: Dispel magic ends a spell on one target. It doesn’t end the same spell on other targets.
This line of reasoning can clearly be extrapolated to your situation. The somewhat surprising official answer is that dispel magic should only end the effect on one of the targets - and not both.
You, of course, are always free to rule as you wish at your own table.