Roundup (glyphosate) is a very efficient and safe chemical but you do need to follow the instructions to make it work properly. It is not cheap.
There needs to be a good growth of green leaf for the weeds to absorb it.
The leaves must be dry when you apply it.
There should be a period of 6 hours without rain after it is applied.
Once the leaves are dry you can plant seeds or transplants into the soil immediately as long as you do not cut up the weeds when cultivating because this may stop the chemical getting down to the roots.
If seeds or potatoes have not emerged you can apply to any weeds above ground without harm to your crop. Be careful, some shoots may be nearer to the surface than you thought and can get caught, especially on a rough seedbed where the chemical may penetrate between the clods.
After 10 days the chemical will have travelled as far into the weeds as it is going to. At this point you can dig and cut up the weeds whether they have started to turn yellow or not.
Roundup attacks from the root up and the typical yellowing of the growing tips is the result of the root system failing.
Roundup is not very good on nettles. Sometimes it kills them but often they need a second dose.
Sometimes sprayed plots apparently recover. Often the apparenty recovering weeds are in fact weeds that were dormant or buried at the time of spraying and have started to grow. The result is the same, you need to apply another dose.