Altitude numbers is different BUT the LATITUDE is the same: 6.2° S.
This is incorrect. You need to check again. Be more careful this time.
This makes a question: Is the altitudes numbers valid, or can timeanddate.com be a reliable reference?
The altitude numbers are right (per Stellarium). The difference in solar altitude at local solar noon for these two cities is what is expected, given their latitudes.
At least for globe model, it will be disqualified if the day time is different for two locations with the same latitudes.
Are they really at the same latitude? Check. What timeanddate.com shows is what the globe model predicts.
BTW, the sunrise/transit/sunset times are shown by timeanddate.com with a resolution of one minute. Working in minutes instead of hours:
Jakarta:
Sunrise 5h × 60 m/h + 26m = 326m
Meridian 11h × 60 m/h + 38m = 698m
Sunset 17h × 60 m/h + 51 = 1071m
Morning sun: 698m - 326m = 372m = 6h 12m
Afternoon sun: 1071m - 698m = 373m = 6h 13m
Day length = 1071m - 326m = 745m = 12h 25m
Medellin:
Sunrise 5h × 60 m/h + 53m = 353m
Meridian 11h × 60 m/h + 48m = 708m
Sunset 17h × 60 m/h + 42m = 1062m
Morning sun: 708m - 353m = 355m = 5h 55m
Afternoon sun: 1062m - 708m = 354m = 5h 54m
Day length = 1062m - 353m = 709m = 11h 49m
Both differences are one minute, the limit of your resolution.
For Jakarta on Nov 22 daylength listed in the table is 12h 25m 21s, which rounds to 12h 25m. This is 14s longer than the previous day and 13s shorter than the next.
For Medellin on Nov 22 daylength listed in the table is 11h 48m 48s, which rounds to 11h 49m. This is 11s shorter than the previous day and 11s longer than the next.
Your calculated 0.016h differences between morning and afternoon lengths in the same city are mostly rounding errors due to the times specified to the nearest minute [and truncated to 0.016h = 0.96m = 58s in your calculations but are actually one minute, which is why it's better to work in integer minutes instead of decimal-fraction hours]. In reality, morning and afternoon differ by a few seconds (probably around 6 seconds), not a full minute, with a shorter morning, longer afternoon in Jakarta, and longer morning, shorter afternoon in Medellin. The rounding errors happened to break in the right direction for both cities on this particular day, but wouldn't always do so.
Besides... how could there even be sunrises and sunsets if the earth were flat?