I have finally resolved the issue. In fact, there wasn't any issue at all.

An application pool defined with 4 worker processes would represent 4 Task Manager processes. Each would go through the Application_Start() at first.

Basically, what would make ASP.NET to execute the Application_Start() event more than 4 times if I only defined 4 worker processes in the application pool?

The application pool is linked to two applications. This represents two websites. Thus, multiplying the application pool number of worker processes by the number of applications (websites), that results in 8 ASP.NET application starts .

When the application starts, I log a record in an IISApplicationCycle table. This logs the Task Manager process ID.

Thus, this looks like this:

Task Manager
Process ID: 5680
Process ID: 1428
Process ID: 6964
Process ID: 364

My IISApplicationCycle table
Showing the 4 running worker processes twice
Started at: 30/03/2019 13:07:10.124 Process ID: 6964
Started at: 30/03/2019 13:05:15.197 Process ID: 1428
Started at: 30/03/2019 13:05:12.547 Process ID: 364
Started at: 30/03/2019 12:55:55.207 Process ID: 5680
Started at: 30/03/2019 12:55:30.677 Process ID: 1428
Started at: 30/03/2019 12:55:29.787 Process ID: 6964
Started at: 30/03/2019 12:55:23.630 Process ID: 364
Started at: 30/03/2019 12:55:22.910 Process ID: 5680

My equivalent Hit record for each of those definitions shows that 4 records belong to one site and another 4 records belong to another site.

Thus, each occurence of the same IIS application pool worker process (Task Manager process ID) shown above are linked to both websites. Thus, each worker process fires the application start event for each website.