Unit tests do not run when you install a managed package, but the code coverage of the unit tests of a managed package do affect the overall coverage of your entire unit test coverage.
Unit tests in a managed package can fail when you install a package and still the package will install, but when a package is being created all unit tests need to pass in the org that the package is created.
So unit tests of a managed package must be written well creating their own test data etc, because otherwise all other unit tests in an org may have coverage over 75% but code cannot be deployed because unit tests in managed packages are much lower than 75%
