A recent change in the application however had me refactor out some of the classes I'd added aspects to, to another assembly in the same application. After the refactoring I also added the PostSharp dll to the new project and realized my aspects weren't added/weaved in during the build. This had me thinking, since I did add the PostSharp dll to the new project. After some searching, I found the source of the problem.
Since PostSharp adds extra functionality during your build, you'll need to tell your project (or the C# compile process, that is) to execute this extra PostSharp funcationality. The nuget package actually added this to my original project, but not to any other project in the same solution. So, to solve this, either rerun the nuget package installer on the other project, or, just as easy, add the following xml tag to your csproj file (somewhere at the bottom).
<Import Project="..\packages\PostSharp.18.104.22.168\tools\PostSharp.targets" />
You get this explanation as well in your projects' properties. You will notice an extra PostSharp tab there, that is either enabled - if PostSharp is doing its' thing - or disabled - if it is not, which was the case for me.