You might need to re-install mod. I have not seen this problem with mods you have installed locally, so that will help. However, consider that Steam needs a way to propagate changes:
- takes time to download/receive notification
- new changes would be applied on a new start of game
- due to mix of various mods some files would be recognized as already updated

To reduce amount of conflicts move your files into separate resource directory. It is more work, but you can use includes to bring your changes to files you need.

Originally posted by MrThirtyOddSix:

You might need to re-install mod. I have not seen this problem with mods you have installed locally, so that will help. However, consider that Steam needs a way to propagate changes:
- takes time to download/receive notification
- new changes would be applied on a new start of game
- due to mix of various mods some files would be recognized as already updated

To reduce amount of conflicts move your files into separate resource directory. It is more work, but you can use includes to bring your changes to files you need.

Separate directory? As in not the mod folder?

It did finally change, but it took forever and a day.

Yes, separate directory that is named after your mod, something like /properties/my-cool-unique-mod

This is a way, but in certain cases it is not possible such as textures or models. It should work good if you have very particular changes like new units, or UI text that you want to introduce. And becomes a bit complicated with overriding existing stuff.