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MVC and n-tier architecture are as the name of the last implies ARCHITECTURAL patterns (not even mutualy exclusive).
Singleton is a DESIGN pattern.
In an application with a certain architecture you can use any number of design patterns, according to the application’s use cases. This use cases make one or more design patterns optimal for implementing them.
In case of the Singleton, if you think there should be only one instance of that class in your application then you use it, if multiple instances are needed or more suitable, you don’t. This is the only criteria.
So no, you did not do nothing wrong,
Source:stackexchange.com