One other thing, cars often stop when they have a green light on an intersection that is using timed traffic lights.

Not stopping sometimes happens if the road segments connected to the junction are too small - the AI doesn't have time to stop the vehicles. Either make the segments longer, or reduce their speed limit.

For cars stopping on green lights, check that you don't have any stop/yield signs at the junction (including vanilla game stop sign from Traffic Routes info view > Junctions tab).

The cars still stop when they have a green light. Do you think it has something to do with custom roads? It appears to only happen on roads that are not vanilla.