What was the theory referred to when Reagan embraced the idea through tax incentives?

"Trickle down economics".

In the 1980s, broadly-accepted economic theory supported the idea that the Federal government could stimulate economic growth directly by increased spending and indirectly by a monetary policy aimed to reduce interest rates and thus, encourage increased private investment.

President Reagan wanted to add tax incentives to the list. He advocated a stimulation package of which the primary component was tax reductions that primarily benefited the wealthy.

What about the middle class and lower class, occupied by workers?

Reagan's economic advisers relied on economic theory to explain that lower income individuals would eventually benefit from incentives: The wealthy would spend the money saved on taxes on private goods and services. This increased demand would lead to new jobs and to increased income to the working class, .... eventually.

Thus, Reagan's opponents termed his policies to be "trickle down economics." Give money to the rich and the poor would eventually benefit by the ripples of their spending.