Long-term visa expiration + Count towards Schengen tourist days?

I am an American citizen living in Poland for 6 months.

I arrived in Poland on February 1, 2016 without a Visa. The count toward my Schengen days began. I received my Work Visa for Poland on April 7, 2016. The work visa expires on July 7th. I intend to stay in Poland until July 30, 2016 (which is 180 days after I entered on February 1)

My question is, do the days that I am on a Work Visa count toward my "90 days within a 180 day period" as a tourist? And when my work visa expires on July 7th, will I be able to remain in Poland until July 30?

February 1 -> April 7 = 66 days July 7 -> July 30 = 23 days Total days as a tourist = 89 days