Do positive and negative selection occur simultaneously?

No, positive selection occurs first and is followed by negative selection. 

During positive selection, only T cells that can bind to MHC (Major Histocompatibility Complex) molecules pass the selection test are kept alive and go on to differentiate into mature functional T cells. T cells that cannot bind to MHC are effectively non-functional and are killed by an apoptotic signal to prevent them from entering the body and crowding out functional T cells. Negative selection, which follows positive selection, prevents the development of T cells that might recognize and attack the body's own healthy cells, causing autoimmune diseases.